利用梯行法計算(exp(-pow(x,2)/2)) / sqrt(2*3.14159) , x=-5.0 to 5.0 的積分值

範例 EX4-3 梯行法求 (exp(-pow(x,2)/2)) / sqrt(2*3.14159) ,  x=-5 to 5 

/* ex4-3.c based on Trapezoidol Rule is
 * used for computing definite integral with
 * domain [a,b] with n even-grids.
 */
#include <stdio.h>
#include <math.h>
#define PI   3.141596
#define  F(x)   (1.0/exp(x*x/2))
void main()
{
   int n,i;
   double  a,b,x,tn,h ,sum=0.0;
   scanf("n=%d a=%lf b=%lf",&n,&a,&b);
   h=(b-a)/n;
   x=a;
   for(i=1;i<=n-1;i++)
   {
      x=x+h;
      sum=sum+F(fabs(x));
   }
   tn=(1.0/sqrt(2*PI))*(h/2.0)*(F(fabs(a))+F(fabs(b))+2.0*sum);
   printf("T%d=%10.6lf\n",n,tn);
   return;
}

輸入資料

n=100 a=-5.0 b=5.0

輸出資料

T100=  0.999999