#include <iostream>

#include <cmath>

#include <fstream>


using namespace std;



double functionUnderIntegral(double x) {

	return  (2 * (x*x*x) + cos(x));


}



double rightRectangleMethod(double a, double b, double n, double h) {

	double x;

	double sum = 0;


	for (int i = 1; i <= n; i++) {

		x = a + i*h;

		sum += h*functionUnderIntegral(x);

	}

	return sum;

}



double leftRectangleMethod(double a, double b, double n, double h) {

	double x;

	double sum = 0;


	for (int i = 0; i <= (n - 1); i++) {

		x = a + i*h;

		sum += h*functionUnderIntegral(x);

	}

	return sum;

}



double centralRectangleMethod(double a, double b, double n, double h) {

	double x;

	double sum = 0;


	for (int i = 0; i <= (n - 1); i++) {

		x = a + i*h;

		sum += h*functionUnderIntegral(x + (h / 2));

	}

	return sum;

}



double trapeziumMethod(double a, double b, double n, double h) {

	double x;

	double sum1 = 0;

	double sum2 = 0;


	for (int i = 1; i <= (n - 1); i++) {

		x = a + i*h;

		sum1 += functionUnderIntegral(x);

	}


	sum2 = (h / 2)*(functionUnderIntegral(a) + functionUnderIntegral(b)) + h*sum1;


	return sum2;

}



double simpsonMethod(double a, double b, double n, double h) {

	double x;

	double sum1 = 0;

	double sum2 = 0;

	double sum3 = 0;


	for (int i = 1; i <= (n - 1); i++) {

		if ((i % 2) != 0) {

			x = a + i*h;

			sum1 += functionUnderIntegral(x);

		}

	}


	for (int i = 2; i <= (n - 2); i++) {

		if ((i % 2) == 0) {

			x = a + i*h;

			sum2 += functionUnderIntegral(x);

		}

	}


	sum3 = (h / 3)*(functionUnderIntegral(a) + functionUnderIntegral(b) + 4 * sum1 + 2 * sum2);

	return sum3;

}



double analyticalMethod() {

	return 2 * pow(3.14,3.0) - 1 ;


}



int main()
{


	double a = 0;

	double b = (3.14 / 2);

	double n;

	double h;


	cout << "n := "; cin >> n;
	cout << endl;


	h = (b - a) / n;


	cout << "Right Rectangle Method := " << rightRectangleMethod(a, b, n, h) << endl; cout << endl;

	cout << "Central Rectangle Method := " << centralRectangleMethod(a, b, n, h) << endl; cout << endl;

	cout << "Left Rectangle Method := " << leftRectangleMethod(a, b, n, h) << endl; cout << endl;

	cout << "Trapezium Method := " << trapeziumMethod(a, b, n, h) << endl; cout << endl;

	cout << "Simpson Method := " << simpsonMethod(a, b, n, h) << endl; cout << endl;

	cout << "Analytical Method := " << analyticalMethod() << endl; cout << endl;
	system("pause");


	return 0;

}