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

#define N 1000

double f(double x)
{
	return 1/x;
}

int main(void)
{
	int i;
	double h,soma=0.0f,a=0.1;

	h=(1.0-a)/N;

	for (i=0;i<N;i++)
	{
		double x1 = a + h*i, x2= a + h*(i+1);
		soma += (h/2)*(f(x1) + f(x2));
	}

	double e = fabs((-log(a)-soma)/-log(a));

	printf("Valor calculado: %.15e \nValor real: %.15e \n",soma,-log(a));
	printf("Erro: %e % \n",e*100);

	return 0;
}

// erro = 1/12 * h^2 * [f'(a) - f'(b)]