How to implement Trapezoidal Integration with Infinite Limits in C?

Question

I am trying to create a c program to integrate sin(x)/sqrt(x) between 0 and Infinity. I am using the trapezium rule by cutting off the end points as the function tends to infinity.

However the total returned is too high and I am not sure why. Here's the code:

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

double func(double u)
{ double a;
  a = ((sin(u))/(sqrt(u)));
  return a;}

void main()
    {
    int i, N;
    double sum, u, a, b, h, Fa, Fb, F;

    printf("Enter value of N\n");
    scanf("%d" ,&N);

    a=0.01;
    b=1000;

    h=(b-a)/(N-1);

    sum=0;
    F=func(a);
    u=a;

    for(i=0; i<N; i++)
    {
            sum=sum+F;
            u=u+h;
            F=fabs(func(u));
    }

    Fa=func(a);
    Fb=func(b);

    sum=sum-(0.5*Fa)-(0.5*Fb);
    sum=sum*h;

    printf("I: %lf\n", sum);
}

Any thoughts?

Answer 1

working example: http://ideone.com/Xibrov

just remove the fabs in the line F=fabs(func(u));.

and you should use int main(void) and return 0; at the end instead of void main().