Newton Backward Interpolation Formula

The Simpson’s 3/8th rule was developed by a mathematician named Thomas Simpson. Integration is the process of measuring the area under a function plotted on a graph.

The Simpson’s 3/8th rule is used in complex numerical integrations. This integration method uses parabolas to approximate each part of the curve. It is basically used to measure an area in a curve.

The Simpson’s 3/8th method is used for uniformly sampled function integration purpose. The Simpson’s 3/8th integration method is primarily used for numerical approximation of definite integrals.

Simpson’s Rule Formula

C programming For simpson 3/8th 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,sum3,sumr;

    sum3=sumr=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%3==0)

       {

       sum3=sum3+(2*y[i]);

       }

     else

       {

       sumr=sumr+(3*y[i]);

       }

    }

    printf("The Output is %f",3*h/8*((y[0]+y[n-1])+sum3+sumr));

    return 0;

}