#include "stdafx.h"
#define _USE_MATH_DEFINES
#include <iostream>
#include <cmath>

using namespace std;

double f(double x);
double metoda_trapezow(double a, double b, int n);
double metoda_simpsona(double a, double b, int n);
double metoda_kwadratur(double a, double b, int n);

int main()
{
	cout << metoda_trapezow(0, M_PI, 2000) << endl;
	cout << metoda_simpsona(0, M_PI, 1000) << endl;
	cout << metoda_kwadratur(0, M_PI, 400) << endl;
    return 0;
}

double f(double x) {
	return sin(x);
}

double metoda_trapezow(double a, double b, int n) {
	double h = (b - a) / n;
	double sum = 0;
	double podstawa_1 = f(a);
	double podstawa_2;
	for (int i = 0; i < n; i++) {
		podstawa_2 = f(a + h * i);
		sum += (podstawa_1 + podstawa_2);
		podstawa_1 = podstawa_2;
	}
	return 0.5 * sum * h;
}

double metoda_simpsona(double a, double b, int n) {
	double h = (b - a) / n;
	double xi = a;
	double xi1, ti;
	double sum = 0;
	for (int i = 0; i < n; i++) {
		xi1 = a + i * h;
		ti = (xi + xi1) / 2;
		sum += ((xi1 - xi) / 6) * (f(xi) + f(xi1) + 4 * f(ti));
		xi = xi1;
	}
	return sum;
}

double metoda_kwadratur(double a, double b, int n) {

	int ng = 1;
	double h = (b - a) / (n - 1);

	double psi[2];
	psi[0] = -sqrt(1 / 3); psi[1] = -psi[0];
	double w[2];
	w[0] = 1.0; w[1] = 1.0;
	double calka = 0; double sum = 0;
	double xi = a;
	double xi1;
	for (int i = 0; i < n; i++) {
		sum = 0;
		xi1 = a + i * h;
		for (int j = 0; j <= ng; j++) {
			psi[j] = ((xi1 - xi) / 2) * f((xi1 + xi) / 2 + (xi1 - xi) / 2 * psi[j]);
			sum += psi[j] * w[j];
		}
		xi = xi1;
		calka += sum;
	}

	return calka;
}