This C# Program Finds Value of 1/(1+x2) using Simpsons 1/3 Rule. Here Simpson’s 1/3 Rule Numerical Integration is used to estimate the value of a definite integral. It works by creating an even number of intervals and fitting a parabola in each pair of intervals.

Here is source code of the C# Program to Find Value of 1/(1+x2) using Simpsons 1/3 Rule. The C# program is successfully compiled and executed with Microsoft Visual Studio. The program output is also shown below.

`/*`

`* C# Program to Find Value of 1/(1+x2) using Simpsons 1/3 Rule`

`*/`

using System;

`class simpson`

`{`

float a, b;

int n;

public void readdata()

`{`

Console.WriteLine("Enter the Lower Limit Value : ");

a = Convert.ToSingle(Console.ReadLine());

Console.WriteLine("Enter the Upper Limit Value : ");

b = Convert.ToSingle(Console.ReadLine());

Console.WriteLine("Enter the Number of Intervals : ");

n = Convert.ToInt32(Console.ReadLine());

`}`

public void simp()

`{`

int i;

float x, sum = 0.0f, h;

float[] y = new float[n + 1];

h = (b - a) / n;

x = a;

for (i = 0; i <= n; i++)

`{`

y[i] = 1.0f / (1 + x * x);

x = x + h;

`}`

sum = y[0] + y[n];

for (i = 1; i < n - 1; i += 2)

`{`

sum += 4 * y[i]+2* y[i + 1];

`}`

sum = sum * h / 3.0f;

Console.WriteLine("Integral Value : {0} ", sum);

Console.ReadLine();

`}`

public static void Main()

`{`

simpson obj = new simpson();

obj.readdata();

obj.simp();

`}`

`}`

Here is the output of the C# Program:

Enter the Lower Limit Value : 1 Enter the Upper Limit Value : 10 Enter the Number of Intervals : 100 Integral Value : 0.6845199

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