#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;

double f(double x);

int main()
{
	int a,b,k,n,i;
	double Tzero;
	double Tk;
	double deltaX;
	double sumDeltaX;

	cout << "Input 2 numbers for the range of your integral:\n";
	cin >> a >> b;


	Tzero = 0.5*(f(a)+ f(b))*(b - a);
	Tk = Tzero;

	cout << "\n    k           Tk  \n";
	cout << "--------------------\n";
	cout<< "    " << 0 << "       " << fixed << Tzero << endl;
	for(k=1; k<=8; k++)
	{
		n =(pow(2.0,k));
		deltaX = (static_cast<double>(b)-static_cast<double>(a))/static_cast<double>(n);

		sumDeltaX = 0;

		for(i=1; i<=(n-1); i=i+2)
		{
			sumDeltaX = sumDeltaX + f(a + i*deltaX);
		}

		Tk = 0.5*Tk + deltaX * sumDeltaX;
		cout << "    " << k << "       " << fixed << Tk << endl;
		sumDeltaX = 0;
	}

	return 0;
}