math - double integration using rectangular method in C -

i know how can calculate double integral shown in picture below

i need calculate in c using rectangular method know how calculate integral not double 1 have calculated above integral in c integral(1/(1+x^2)) x 0 1 not understand how should proceed further

if can point me right direction on how should approach solution.

you can use definition of (cascading) riemann integral:

int n = 5000;//or large number, discretization step double dxy = 1.0d/n; double integral = 0.0d; for(int yi = 0; yi < n; yi++) {     double y = yi*dxy; //the y-value     for(int xi = 0; xi < n; xi++) {         double x = xi*dxy; //the x-value         integral += 1.0d/(1.0d+x*x+y*y); //function call     } } return integral*dxy*dxy; 

in other words, calculate integral like: