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

#define del 1e-5

double f(double x)
{
	return 1/x; // função a ser integrada
}

int main(void)
{
	int N = 10;
	double h, I, Iold, eps;

	// ------------------------- I_1 -------------------------

	int i;
	double 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));
	}

	I = soma;

	// ------------------------- END -------------------------

	do {
		Iold = I;
		N = 2*N;
		h = h/2; // otimizando!

		double soma = 0; // importante zerar somaaa!!!

		for(i = 1; i < N; i += 2) 
		{
			soma += f(a + i*h);
		}

		I = 0.5*Iold + h*soma;

		eps = 1.0/3 * fabs(I - Iold);

		printf("%d %e\n", N, eps);
	} while (eps > del);

	return 0;
}

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