I think I'm doing everything correctly but for some reason the program refuses to compute, it just freezes.

I'm given an equation for a curve, and for certain values of x and y along that I want to take the double integral and set that over the double integral of the whole curve and compute that fraction.

To do this I loop through values of x and y and then multiply them to get the double integral of the whole curve.

For the isolated section of the curve I substitute a new variable z for y and then within the x loop I cycle through z values for each value of x and if x and z are within certain values I compute the smaller integral.

I then set the two integrals over each other and compute that fraction.

What am I doing wrong?

Code:

#include <stdio.h>
#include <math.h>
#define STEP 5.556e-5
int main() {
float a=0.3489, b=0.255, R=0.68085, xlimit=0.2799, zlimit=-0.0008;
float utotalarea=0;
float vtotalarea=0;
float x, xarea, xtotalarea=0;
float y, yarea, ytotalarea=0;
float z, zarea;
float result, result2, fraction;
//First loop through x values.
for (x=STEP; x<=10; x=x+STEP){
xarea=0.5*(exp(-log(2)*pow(x/a,2)-1)+exp(-log(2)*pow((x-STEP)/a,2)-1))*STEP;
xtotalarea=xtotalarea+xarea;
//Next, loop through z values for each x value. Note: z is really y, its a different variable here in order to calculate the integral for certain x and y values.
for (z=STEP; z<=10; z=z+STEP){
zarea=0.5*(exp(-log(2)*pow(z/b,2)-1) + exp(-log(2)*pow((z-STEP)/b,2)-1))*STEP;
//If x and z are within certain values take integral.
if((pow(x-xlimit,2)+pow(z-zlimit,2))<=pow(R,2)){
utotalarea=utotalarea+xarea;
vtotalarea=vtotalarea+zarea;
}
}
}
//Now, loop through all y values.
for (y=STEP; y<=10; y=y+STEP){
yarea=0.5*(exp(-log(2)*pow(y/b,2)-1)+exp(-log(2)*pow((y-STEP)/b,2)-1))*STEP;
ytotalarea=ytotalarea+yarea;
}
//Compute double integral for the whole curve.
result=xtotalarea*ytotalarea;
//Compute double integral for the certain x and z values.
result2=utotalarea*vtotalarea;
//Set the smaller integral over the larger integral.
fraction=result2/result;
//print the fraction.
printf("%.5f\n", fraction);
}