Newton Backward Interpolation Formula

Trapezoidal Rule using C programming :


In mathematics, the trapezoid rule is a numerical integration method, that is, a method to calculate approximately the value of the definite integral.

The Formula is :

                    

=

=h/2[(y0+yn)+2*(y1+y2+y3+y4+......+yn-1)]

or 

h/2[(X)+2*R];

Where X =y0+y1

           R= y1+y2+y3+........................yn-1

Trapezoidal Rule using C programming :

#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,sum;

    sum=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++)

    {

       sum=sum+(2*y[i]);

    }

    printf("The Output is %f",h/2*((y[0]+y[n-1])+sum));

    return 0;

}