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

double f(double x)
  {
    double fx;
     
     fx=sin(x);
     return fx;
  }

double trapezoid(double x1, double x2, int n) 
  {
    double x,fx,s;
    int i;
    s=0.0; s=s+f(x1);
    for (i=1;i<n;i++) {
		x=x1+(x2-x1)/(double) n*(double) i; 
        fx=f(x);
        s=s+2.0*fx;
        }
    s=s+f(x2);s=s/2.0*(x2-x1)/(double) n;
    return s;
 }

double simpson(double x1, double x2, int n) 
  {
    double xx1,xx2,fx1,fx2,s;
    int i;
    s=0.0; s=s+f(x1);
    for (i=1;i<=n/2;i++) {
		xx1=x1+(x2-x1)/(double) n*(double) (i*2-1); 
        fx1=f(xx1);
		xx2=x1+(x2-x1)/(double) n*(double) (i*2); 
        fx2=f(xx2);
        s=s+4.0*fx1+2.0*fx2;
        }
    s=s-f(x2);s=s/3.0*(x2-x1)/(double) n;
    return s;
 }
 
int main() 
  {
    double x1,x2,s1,s2;
    int n,j;
    x1=0.0;x2=4.0*atan(1.0);n=8;
    for (j=1;j<=7;j++) {
     n=n*2;
     s1=trapezoid(x1,x2,n);
     s2=simpson(x1,x2,n);
     printf("n= %4d, trapezoidal %20.13lf simpson = %20.13lf\n",n,s1,s2);
     }
 }