Code for Simpson's 1/3 rule

#include <stdio.h>

#include <conio.h>

#include <math.h>

float f(float x)

{

  return (sqrt(sin(x)));

  //f(x)=sqrt(sin(x));

}

void main()

{

  float a,b,h,x,sum=0;

  int n,i,k;

  printf("Enter a and b: ");

  scanf("%f%f",&a,&b);

  printf("Here, n=2 for Simpson's 1/3 rule");

  printf("\nn>2 for Composite Simpson's 1/3 rule\n");

  printf("So, Enter n: ");

  scanf("%d",&n);

  h=(b-a)/n;

  for(x=a,i=0,k=1;x<=b,i<=n;x=x+h,i++,k=k+2)

  {

    if(i==0||i==n)

      sum=sum+f(x);

    else if(i==k)

      sum=sum+4*f(x);

    else

      sum=sum+2*f(x);

  }

  sum=h/3*sum;

  printf("\nI=%f",sum);

  getch();

}

OUTPUT:

Simpson’s 3/8 Rule >>