Simpson 1/3rd Rule using C programming

The Simpson’s 1/3rd integration method is primarily used for numerical approximation of definite integrals. This specifically means that Simpson’s integration rule is used in complex integration calculations.

It is a method to approximately calculate the definite integral. The Simpson’s theorem is used to find the area under a given curve. The Simpson’s method corresponds to the 3-point Newton-Cotes quadrature rule as well.

The Simpson’s integration method is a little time consuming compared to other methods in numerical analysis and is also a little difficult to implement computationally.

Simpson’s Rule Formula

                 

C Programming For Simpson 1/3rd Rule :

#include<stdio.h>

int main()

{

    int n,i,j;

    printf("Enter the total Number of Input You want");

    scanf("%d",&n);

    float x[n],y[n],h,sume,sumo;

    sume=sumo=0;

    for(i=0;i<n;i++)

    {

        printf("Enter the value of X[%d] : ",i);

        scanf("%f",&x[i]);

    }

    for(i=0;i<n;i++)

    {

        printf("Enter the value of Y[%d] : ",i);

        scanf("%f",&y[i]);

    }

    h=((x[n-1]-x[0])/(n-1));

    for(i=1;i<n-1;i++)

    {

     if(i%2==0)

       {

       sume=sume+(2*y[i]);

       }

     else

       {

       sumo=sumo+(4*y[i]);

       }

    }

    printf("The Output is %f",h/3*((y[0]+y[n-1])+sumo+sume));

    return 0;

}