simpson.c

// C code to implement SIMPSON'S  1/3  RULE

#include<stdio.h>
#include<math.h>

float f(float x){
      return(1/(1+pow(x,2)));
}

int main(){
        int n,i;
        float s1=0,s2=0,sum,a,b,h;

        printf("Enter the value of upper limit = ");
        scanf("%f",&b);
        printf("Enter the value of lower limit = ");
        scanf("%f",&a);
        printf("Enter the number of intervals = ");
        scanf("%d",&n);

        h=(b-a)/n;

        if(n%2==0){
                for(i=1;i<=n-1;i++)
                        if(i%2==0)
                                s1=s1+f(a+i*h);
                        else
                                s2=s2+f(a+i*h);

                sum=h/3*(f(a)+f(b)+4*s2+2*s1);
                printf("the value is = %f\n",sum);
        }
        else
                printf("the rule is not appliciable\n");
}

/*********************************************************************************
 * OUTPUT:
 * Enter the value of upper limit = 1
 * Enter the value of lower limit = 0
 * Enter the number of intervals = 10
 * the value is = 0.785398
 * ******************************************************************************/