// ==================================================================
//      Author: Jean-Michel RICHER
//       Email: jean-michel.richer@univ-angers.fr
// Institution: LERIA, Faculty of Science 
//              University of Angers, France
// ==================================================================

// Compute integral of function f(x) = x^2 between X_0 and X_1
// using area of rectangles 

#include <iostream>
#include <cmath>
using namespace std;

typedef double real;

real X_0  = 1.0;
real X_1  = 3.0;
int STEPS = 1'000'000;

/* ==================================================================
 * SUBPROGRAM
 *
 *		real f(real x ;
 *
 * WHAT
 *
 *  Function to integrate
 *
 *
 * PARAMETERS
 *
 *	@paramdef(real, x) : abscissa
 *
 * ==================================================================
 */
real f( real x ) {
    return x * x;
}

/* ==================================================================
 * SUBPROGRAM
 *
 *		real integrate(real x_0, real x_1, int steps)
 *
 * WHAT
 *
 *  Use the sum of rectangles under the function
 *
 * HOW
 *
 *	We compute the sum of (x_1 - x_0) / steps rectangles
 *
 * PARAMETERS
 *
 *	@paramdef(real, x_0) : lower bound
 *  @paramdef(real, x_1) : upper bound
 *  @paramdef(int, steps) : number of rectangles to use
 *
 * RETURN VALUE
 *
 *  @return(real) the sum of all rectangles that compose the
 *  integral
 *
 * ==================================================================
 */
real integrate(real x_0, real x_1, int steps) {

	real dx, local;
	real  delta_x = (x_1 - x_0) / steps;
	
	real area = 0;
	for (int i = 1; i <= steps; ++i) {
		area += f(x_0 + i * delta_x);
	}
	
	return delta_x * area;
}

/* ==================================================================
 * SUBPROGRAM
 *
 * 		int main(int argc, char *argv[])
 *
 * WHAT
 *
 *   Main program
 *
 * PARAMETERS
 *
 *	@paramdef(int,argc) : number of command line arguments
 *  @paramdef(char **, argv) : command line arguments as C-strings
 *
 * ==================================================================
 */
int main() {

	cout << "integrate(" << X_0 << ", " << X_1 << ")=" << integrate(X_0, X_1, STEPS) << endl;
	
	return EXIT_SUCCESS;
}