Simpson’s 3/8th Rule is a Numerical technique to find the definite integral of a function within a given interval.

It’s so called because the value 3/8 appears in the formula.

The function is divided into many sub-intervals and each interval is approximated by a cubic curve. And the area is then calculated to find the integral. The more is the number of sub-intervals used, the better is the approximation.

### FORMULA:

where,

where starts from 0 and goes to

NOTE: The no. of sub-intervals , should be a multiple of 3 for this method.

### PROGRAM:

/********************************* *******SIMPSON'S 3/8 RULE******** ********************************/ #include<stdio.h> #include<math.h> double f(double x){ return x*x; } main(){ int n,i; double a,b,h,x,sum=0,integral; printf("\nEnter the no. of sub-intervals(MULTIPLE OF 3): "); scanf("%d",&n); printf("\nEnter the initial limit: "); scanf("%lf",&a); printf("\nEnter the final limit: "); scanf("%lf",&b); h=fabs(b-a)/n; for(i=1;i<n;i++){ x=a+i*h; if(i%3==0){ sum=sum+2*f(x); } else{ sum=sum+3*f(x); } } integral=(3*h/8)*(f(a)+f(b)+sum); printf("\nThe integral is: %lf\n",integral); }