/***********************************************************************
 * 
 * File: gauss5.c (30-Mar-2001)
 *                (24-Mar-2006)
 *                (20-Mar-2008)
 * 
 * Numerische Integration der Funktion
 * 
 *   f(x) = exp(x)
 * 
 * mit der 5-Punkt Gauss-Legendre Formel
 * 
 * a,b...Intervallgrenzen
 * 
 **********************************************************************/

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

#define N 5
const float w[N]={0.236927,0.478629,0.568889,0.478629,0.236927};
const float x[N]={-0.90618,-0.538469,0.0,0.538469,0.90618};

/**********************************************************************/

float f(float x) {

/**********************************************************************/

  return exp(x);

}

/**********************************************************************/

int main() {

/**********************************************************************/

  int i;
  float a,b,s;

  printf(" a,b=");
  scanf("%f,%f",&a,&b);
  
  s=0.0;
  for(i=0;i<=N-1;i=i+1) {
    s=s+w[i]*f(0.5*(a+b+x[i]*(b-a)));
  }
  s=0.5*s*(b-a);

  printf(" s=%14.7e (%14.7e)\n",s,exp(b)-exp(a));

  return 0;

}

/**********************************************************************/