Trying to add array elements gives zero

Question

So I've been trying to implement a small program to calculate double integral using simpsons 1/3 rule for a college assignment using the obsolete turbo c++ compiler (yes, we still use it!) but sadly I've seem hit a strangle glitch. Whenever I try add elements of array ax[i] in following program that gives me a zero. The elements seem to be showing up perfectly in and of themselves but adding them results in a zero for some strange reason. Here's the piece of code.

#include<iostream.h>
#include<conio.h>
#include<math.h>

double f(double, double);

void main()
{
    clrscr();
    double a, b, c, d, h, k, ans, z[10][10], ax[10];
    int i, j, nx, ny;
    clrscr();
    a=0.0; b=1.0; c=0.0; d=1.8; h=0.25; k=0.30;
    nx = (b-a)/h;
    ny = (d-c)/k;

    for(i=0; i<10; i++)
    {
        for(j=0; j<10;j++)
            z[i][j] = 0;
        ax[i] = 0;
    }

    //Generating the table
    for(i=0; i<=nx; i++)
    {
        for(j=0; j<=ny; j++)
        {
            z[i][j] = f(a+i*h, c+j*k);
        }
    }

    for(i=0; i<=nx; i++)
    {
        ax[i] = 0.0;

        for(j=0; j<=ny; j++)
        {
            if(j==0 || j==ny)
                ax[i] += z[i][j];
            else if(j%2==1)
                ax[i] += 4*z[i][j];
            else
                ax[i] += 2*z[i][j];
        }
        ax[i] *= k/3.0;
        cout<<ax[i]<<endl;
    }

    ans=  1.0;
    //for(int q=0; q<=nx; q++)
        ans= (ax[0])+(ax[1])+(ax[2]);


    cout<<"Value of integral is: "<<ans;
    getch();
}

double f(double x, double y)
{
    float r;
    r = 2*x*y/sqrt(x*x+y*y);
    return r;
}

Ideas?

Answer 1

double f(double x, double y)
{
    float r;
    r = 2 * x*y / sqrt(x*x + y*y);
    return r;
}

Divides by zero when x=0 and y=0, so ax[0] equals nan. When you add the numbers up, you're going to get nan as the output. You need to use L'Hopital's rule to evaluate that limit, and handle the first element differently.