Simpson’s 1/3 Rule Program in C#

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.

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

```
 */
```
```
using System;
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```
 
```
```
class simpson
```
```
{
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```
    float a, b;
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    int n;
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    public void readdata()
```
```
    {
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        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());

```
    }
```
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    public void simp()
```
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    {
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        int i;
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        float x, sum = 0.0f, h;
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        float[] y = new float[n + 1];
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        h = (b - a) / n;
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        x = a;
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        for (i = 0; i <= n; i++)
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        {
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            y[i] = 1.0f / (1 + x * x);
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            x = x + h;
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        }
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        sum = y[0] + y[n];
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        for (i = 1; i < n - 1; i += 2)
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        {
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            sum += 4 * y[i]+2* y[i + 1];

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        }
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        sum = sum * h / 3.0f;
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        Console.WriteLine("Integral Value : {0} ", sum);

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        Console.ReadLine();
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    }
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    public static void Main()
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    {
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        simpson obj = new simpson();
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        obj.readdata();
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        obj.simp();
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    }
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```
}
```

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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