/* 
 * Program to approximate multiple functions using numerical integration.
 */ 
#include <stdio.h>
#include <math.h>

/* 
 * function to perform numerical integration 
 * last parameter is function to integrate
 */
double approx(long nslices, double start, double end, double (*fcn) (double x));

/*
 * some functions to try
 */

/* function we used to approximate pi */
double fcn_for_pi(double x) {
	return 4.0 / (1 + x*x);
}

/* straight line -- y=2 */
double fcn_line(double x) {
	return 2;
}

/* straight line -- y=x*2 */
double fcn_line2(double x) {
	return x * 2;
}

/* main program */

int main(void) {

	long num_slices;
	printf("enter number of slices\n");
	if (scanf("%ld", &num_slices) != 1) {
		printf("not number\n");
		return 1;
	}


	/* call approx function several times to integrate various functions */

	printf("with %ld slices approx pi is %.15f\n", 
			num_slices, approx(num_slices, 0.0, 1.0, fcn_for_pi));

	printf("with %ld slices approx integral of constant line is %.15f\n", 
			num_slices, approx(num_slices, 1.0, 5.0, fcn_line));

	printf("with %ld slices approx integral of sloped line is %.15f\n", 
			num_slices, approx(num_slices, 1.0, 5.0, fcn_line2));
	return 0;
}

double approx(long nslices, double start, double end, double (*fcn) (double x))
{

	double width = (end - start) / nslices;
	double sum = 0.0;

	/* compute heights of rectangles and add */
	for ( int i = 0; i < nslices; ++i) {
		double mid = start + i*width + 0.5*width;
		double f_at_mid = fcn(mid);
		sum += f_at_mid;
	}
	/* area is sum of heights times width */
	return sum * width;
}