Hướng dẫn simpsons 1/3 rule python - trăn quy tắc 1/3 simpsons

Question

Chương trình này thực hiện quy tắc 1/3 của Simpson để tìm giá trị xấp xỉ của tích hợp số trong ngôn ngữ lập trình Python.

Trong chương trình Python này, lower_limit và upper_limit là giới hạn tích hợp thấp hơn và trên, sub_interval là số khoảng thời gian phụ được sử dụng trong khi tìm tổng và chức năng f(x) được tích hợp bằng phương pháp Simpson 1/3 được xác định bằng định nghĩa chức năng Python def f(x):.Simpson 1/3 method is defined using python function definition def f(x):.

Nội dung chính Show

Mã nguồn Python: Quy tắc 1/3 của Simpson
1.8278470 def f(x):2
lower_limit41.8278470 lower_limit85
Enter lower limit of integration: 0 Enter upper limit of integration: 1 Enter number of sub intervals: 6 Integration result by Simpson's 1/3 method is: 0.785398 9sub_interval30 sub_interval31

Mã nguồn Python: Quy tắc 1/3 của Simpson


# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Đầu ra

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

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Hướng dẫn simpsons 1/3 rule python - trăn quy tắc 1/3 simpsons

Trong phân tích số, quy tắc Simpson 1/3 là một phương pháp xấp xỉ bằng số của các tích phân xác định. Cụ thể, đó là xấp xỉ sau: & nbsp;
the area into n equal segments of width Δx.
Simpson’s rule can be derived by approximating the integrand f (x) (in blue)
by the quadratic interpolant P(x) (in red).

& nbsp; & nbsp;
1.Select a value for n, which is the number of parts the interval is divided into.
2.Calculate the width, h = (b-a)/n
3.Calculate the values of x0 to xn as x0 = a, x1 = x0 + h, …..xn-1 = xn-2 + h, xn = b.
Consider y = f(x). Now find the values of y(y0 to yn) for the corresponding x(x0 to xn) values.
4.Substitute all the above found values in the Simpson’s Rule Formula to calculate the integral value.
Approximate value of the integral can be given by Simpson’s Rule:

Bàn luận

Trong phân tích số, quy tắc Simpson 1/3 là một phương pháp xấp xỉ bằng số của các tích phân xác định. Cụ thể, đó là xấp xỉ sau: & nbsp; In this rule, n must be EVEN.
Application :
It is used when it is very difficult to solve the given integral mathematically.
This rule gives approximation easily without actually knowing the integration rules.
Example :

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

C++

#include

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

0

& nbsp; & nbsp;

Trong quy tắc 1/3 của Simpson, chúng tôi sử dụng parabolas để xấp xỉ từng phần của đường cong. & nbsp; bởi nội suy bậc hai p (x) (màu đỏ). & nbsp; & nbsp;

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

Để tích hợp bất kỳ hàm f (x) nào trong khoảng (a, b), hãy làm theo các bước được đưa ra dưới đây: 1. Chọn một giá trị cho n, đó là số phần mà khoảng thời gian được chia thành. & Nbsp; 2.Calculation Chiều rộng, h = (b-a) /n 3 Hãy xem xét y = f (x). Bây giờ tìm các giá trị của y (y0 đến yn) cho các giá trị x (x0 đến xn) tương ứng. được đưa ra bởi quy tắc của Simpson: & nbsp;

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Lưu ý: Trong quy tắc này, n phải chẵn. Ứng dụng: & nbsp; nó được sử dụng khi rất khó để giải quyết tính tích phân đã cho.

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

1

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

2

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

5

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

7

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

1

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

2

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

5

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

7

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

9

1.827847

0

1.827847

1

lower_limit4lower_limit5

lower_limit4lower_limit7

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

5

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

7

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

9

1.827847

0

1.827847

1

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

sub_interval1sub_interval2

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

1.827847

5

sub_interval1sub_interval8

lower_limit4sub_interval4

sub_interval1f(x)2

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9f(x)6

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

1.827847

8

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9lower_limit0 lower_limit1

1.827847

0 lower_limit3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4 upper_limit2

lower_limit4upper_limit9 sub_interval0

lower_limit4sub_interval4 upper_limit9 sub_interval6

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9#include 4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0 f(x)9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

1.8278470 def f(x):2

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4 def f(x):6

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4 def f(x):9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

1.827847

0 #include 2

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0 #include 7

Java

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

#include 9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

00

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

01

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

03

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

5

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

7

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0 lower_limit1

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

14

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

03

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

5

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

7

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

24

sub_interval1lower_limit5

sub_interval1lower_limit7

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

25

1.827847

0

1.827847

1

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

03

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

5

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

7

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

24

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

25

1.827847

0

1.827847

1

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

79sub_interval2

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

1.827847

5

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

35

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

36

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

38

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

39

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

40

sub_interval1sub_interval4

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

43

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

36

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

38

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

39

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

40

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

02

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

03

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

04

lower_limit4lower_limit0 lower_limit1

1.827847

0

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

53

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

54

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

55

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

64

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

54

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

66

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

16

sub_interval1upper_limit9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

76

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

54

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

78

sub_interval1sub_interval4 upper_limit9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

84

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

85

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

86

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

54

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

88

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

79

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

90

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

91

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

92

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

35

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

36

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

37

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Python3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

79

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

90

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

85

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

92

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0 f(x)9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9#include 9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

03

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

13

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

14

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

19

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

91

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

66

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

24

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

88

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

27

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

66

lower_limit4

1.827847

0

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

31

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

32

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

66

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

41

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

42

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

43

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

44

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

47

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

78

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

79

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

69

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

81

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

82

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

84

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

69

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

79

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

89

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

91

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

54

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

69

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

54

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

73

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

74

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

76

lower_limit4___

sub_interval1

1.827847

15

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

79

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

1.827847

18

lower_limit4

1.827847

20

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

69

1.827847

22

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

85

1.827847

24__

sub_interval1

1.827847

15

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

79

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

91

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

81

1.827847

18

lower_limit4sub_interval4

1.827847

27

sub_interval1

1.827847

15

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

79

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

85

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

81

1.827847

18

lower_limit4

1.827847

46

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

79

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

89

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

91

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

91

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

81

1.827847

55__

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0

1.827847

15

1.827847

62

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52 ________ 191 & nbsp; & nbsp;

1.827847

65

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

27

1.827847

68

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

52

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

32

1.827847

71lower_limit1

1.827847

73

1.827847

22

1.827847

75

C#

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

1

1.827847

77

#include 9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

00

1.827847

80

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

03

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

5

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

7

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0 lower_limit1

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

1.827847

94

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

03

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

5

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

7

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

24

lower_limit05

1.827847

0

1.827847

1

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

1.827847

5

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

35

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

36

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4lower_limit18

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

43

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

36

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4lower_limit18

lower_limit4lower_limit0 lower_limit1

1.827847

0 lower_limit3

sub_interval1lower_limit5

sub_interval1lower_limit7

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4 upper_limit2

lower_limit4lower_limit0 lower_limit1

1.827847

0 lower_limit3

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4 upper_limit2

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

79sub_interval2

sub_interval1upper_limit9 sub_interval0

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

79sub_interval8

sub_interval1sub_interval4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

79f(x)2

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit4f(x)6

sub_interval1sub_interval4 upper_limit9 sub_interval6

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0 f(x)9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9#include 9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

03

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

13 lower_limit72

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4 lower_limit77

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

24

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4lower_limit82

lower_limit4lower_limit87

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

36

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

37

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit41.8278470 lower_limit85

lower_limit93

PHP

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

lower_limit94

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

5lower_limit96

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

88

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0 upper_limit01lower_limit96

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

04

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

lower_limit94

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

5upper_limit07upper_limit08upper_limit09____508upper_limit11

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

88

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9upper_limit15 upper_limit16upper_limit09 upper_limit18upper_limit07upper_limit20upper_limit11

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

66

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9lower_limit0 lower_limit1______526

lower_limit4upper_limit48

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

38upper_limit26upper_limit51lower_limit96

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

38upper_limit26upper_limit55

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit4___

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9upper_limit15 upper_limit16upper_limit09 upper_limit18upper_limit07upper_limit20upper_limit11

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

66

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9lower_limit0 lower_limit1______526

lower_limit4___

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9upper_limit59 upper_limit60

lower_limit4upper_limit9 lower_limit1______526

lower_limit4sub_interval4

sub_interval1upper_limit59 upper_limit85upper_limit48

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

38upper_limit26

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

40

lower_limit4sub_interval4 upper_limit9 lower_limit1upper_limit26 upper_limit95

sub_interval1upper_limit59 upper_limit98upper_limit48

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

38upper_limit26

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

40

sub_interval1upper_limit59 sub_interval07upper_limit48

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

38upper_limit26

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

40

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9upper_limit59 sub_interval16upper_limit59 sub_interval18upper_limit15 sub_interval20

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0 upper_limit59

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

66

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9sub_interval27 sub_interval28

sub_interval44

Enter lower limit of integration: 0 Enter upper limit of integration: 1 Enter number of sub intervals: 6 Integration result by Simpson's 1/3 method is: 0.785398 9sub_interval30 sub_interval31

sub_interval45

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9upper_limit11 sub_interval34

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9sub_interval36

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

5sub_interval27upper_limit08____630upper_limit08upper_limit11

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

04

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

JavaScript

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

8

lower_limit4sub_interval62

lower_limit4sub_interval64

lower_limit4sub_interval66

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9lower_limit94 sub_interval48

sub_interval1lower_limit5

sub_interval1lower_limit7

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit4sub_interval77

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9lower_limit94 sub_interval48

lower_limit4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

4 upper_limit2

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

79sub_interval2

sub_interval1upper_limit9 sub_interval0

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

79sub_interval8

sub_interval1sub_interval4

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

79f(x)2

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit4f(x)6

lower_limit4

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

0 f(x)9

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

9

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

3

lower_limit4f(x)06

lower_limit4f(x)08

lower_limit4f(x)10

lower_limit4f(x)12

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

36

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.

37

f(x)15

Output:

1.827847

programming python Simpson Method C++ Simpson rule Simpson rule formula

Hướng dẫn simpsons 1/3 rule python - trăn quy tắc 1/3 simpsons

Chương trình này thực hiện quy tắc 1/3 của Simpson để tìm giá trị xấp xỉ của tích hợp số trong ngôn ngữ lập trình Python.

Mã nguồn Python: Quy tắc 1/3 của Simpson

Đầu ra

C++

1.8278470 def f(x):2

Python3

C#

lower_limit41.8278470 lower_limit85

Enter lower limit of integration: 0 Enter upper limit of integration: 1 Enter number of sub intervals: 6 Integration result by Simpson's 1/3 method is: 0.785398 9sub_interval30 sub_interval31

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