#include <stdio.h>
#include <math.h>
#define KMAX 7
#define PI 3.141592653589793238
double func(double x);

int main(void)
{
  int k = 0, n = 1; 
  double a,b,h,x,s = 0.0, w, I;

  a = 0.0;
  b = 2 * PI;
  I = 7.9549265210128448631;

  h = b-a;
  s = 0.5 * h * (func(a) + func(b));
  k = 0;

  printf("%3s %5s %20s %11s\n","n","h","T_n   ","T_n-I");  
  printf("%3d %8.4f %20.15f %11.4e\n",n,h,s,s-I);

  for(k = 1; k <= KMAX && fabs(s-I)>1.0e-15; k++){
    n *= 2;
    h *= 0.5;
    w = 0.0;
    x = a + h;
    while(x < b){
      w += func(x);
      x += 2.0 * h;
    }
    s = 0.5 * s + h * w;
    printf("%3d %8.4f %20.15f %11.4e\n",n,h,s,s-I);
  }

  return 0;

}

double func(double x)
{

  return exp(sin(x));
}