#include<stdio.h>
#include<stdlib.h>
#include<math.h>
 
typedef double (*FUNC)(double);
 
double integ(FUNC f, const double a, const double b, const int n){
	int i;
	const double dx = (b - a)/n;
	double total = 0.0;
 
	for (i = 0; i < n; i++){
		const double x = -(a + (i+0.5)*dx);
		total += f(x)*dx;
	}
 
	return total;
}
 
int main(void){
	const double a = 0;
	const double b = 0.49;
	const double sval = 1-exp(-b);
	int i;
 
	printf("Integration of exp(-x) for [%.2f, %.2f] and errors\n",a, b);
	for(i = 0; i < 7; i++){
		const int div = (int)pow(10, i);
		const double xi = integ(exp, a, b, div);
		const double err = sval - xi;
		printf("%7d %.15f %.15e\n", div, xi, err);
	}
 
	printf("strict value = %.15f\n", sval);
 
	return 0;
}
 

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