/*
	Calculate the integration of 2 dimensional function
	f(x, y)=sin(x)*sin(y)
	The true integral is cos(1)^2-2*cos(1)+1
*/

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

#define x0 0	//beginning x value
#define xn 1	//ending x value
#define y0 0	//beginning y value
#define yn 1	//ending y value

double f(double, double);

double f(double x, double y)
{
	return sin(x)*sin(y);
}

main(int argc, char** argv) {
	int n;		//number of rectangles
	double h;	//width of each rectangle, (xn-x0)/n
	double sum = 0;
	int i = 0, j = 0;

	printf("Number of rectangles: ");
	scanf("%d", &n);
	h = ((double)(xn - x0) / n);
	printf("x0=%d, xn=%d, y0=%d, yn=%d, n=%d, h=%lf..\n", x0, xn, y0, yn, n, h);

	for (i=0; i<n; i++)
	{
		for (j=0; j<n; j++)
		{
			sum += h * h * f(x0 + i * h, y0 + j * h);
		}
	}

	printf("The area is %lf\n", sum);
	printf("The true area is %lf\n", pow(cos(1), 2) - 2*cos(1) + 1);
}