Simson’s 1/3rd formula (composite)
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define F(x) 1/(1+x*x)
int main (void)
{
int n,i;
float a,b,h,sum1=0.0,sum2=0.0,ics,x,f1,f2,f3,f4;
printf("Initial value of x: ");
scanf("%f",&a);
printf("Final value of x: ");
scanf("%f",&b);
printf("Number of segment(even no): ");
scanf("%d",&n);
h=(b-a)/n;
x=a;
f1=F(x);
for(i=2;i<=n;i=i+2)
{
x=x+h;
f2=F(x);
sum1=sum1+f2;
x=x+h;
}
x=a;
for(i=3;i<n;i=i+2)
{
x=x+2*h;
f3=F(x);
sum2=sum2+f3;
}
x=b;
f4=F(x);
ics=((4*sum1+2*sum2+f1+f4)*h)/3.0;
printf("\nIntegral from %f to %f , \nwhen h = %f is %f",a,b,h,ics);
getch();
return 0;
}