/* Approximate the area under a curve using a Left Riemann Sum
 * Aaron Weeden, NCSI
 * June 28, 2011
*/

#include <stdio.h> /* for printf */

/* Constants */
#define X_LOWER 0.0 /* The lower value of the x-range under which to calculate 
					   the area */
#define X_UPPER 10.0 /* The upper value of the x-range */
#define WIDTH (X_UPPER - X_LOWER) /* The width of the x-range */
#define NUM_RECTANGLES 10 /* The number of rectangles to use in approximation */
#define RECT_WIDTH (WIDTH / NUM_RECTANGLES) /* The width of a rectangle */
float func(float x) /* the curve's function */
{
	return x * x;
}

int main()
{
	/* Variables */
	int i = 0; /* Loop index / rectangle ID */
	float areas[NUM_RECTANGLES]; /* The area of each rectangle */
	float sum = 0.0; /* The total approximated area */

	/* Define the algorithm */
	for(i = 0; i < NUM_RECTANGLES; i++)
	{
		areas[i] = RECT_WIDTH * func(i * RECT_WIDTH + X_LOWER);
	}

	/* Sum the areas */
	for(i = 0; i < NUM_RECTANGLES; i++)
	{
		sum += areas[i];
	}

	/* Print the sum */
	printf("%f\n", sum);

	return 0;
}