Integration

#include "stdafx.h"
#include <iostream>
#include <math.h>

using namespace std;

double gauss_def(double a, double b, float y, float res, double integral);
double simpson_def(double a, double b, float x, float y, float res, double integral, int n);
double trapezoid(double a, double b, float x, float y, float res, double integral, int n);
double three8(double a, double b, float x, float y, float res, double integral, int n);
double def_N2(double a, double b, float x, float y, float res, double integral, int n);

int main()
{
    double a = 0.5, b = 2.5;
    int n = 0, menu = 0;

    double integral = 1.493270847223976;

    float y = 0, res = 0, x = a;
    cout << "Menu\n1.Gauss\n2.Simpson\n3.Trapezoid\n4.3/8\n5.2N\n6.Exit\nEnter: "; cin >> menu; cout << endl;

    if (menu == 1) gauss_def(a, b, y, res, integral);
    if (menu == 2) simpson_def(a, b, x, y, res, integral, n);
    if (menu == 3) trapezoid(a, b, x, y, res, integral, n);
    if (menu == 4) three8(a, b, x, y, res, integral, n);
    if (menu == 5) def_N2(a, b, x, y, res, integral, n);

    //system("pause");
    return 0;
}

double gauss_def(double a, double b, float y, float res, double integral)
{
    double t[] = { -0.90617985 , -0.53846931, 0, 0.53846931, 0.90617985 };
    double A[] = { 0.23692688 , 0.47862868, 0.56888889, 0.47862868, 0.23692688 };

    cout << "| N = 5 |" << endl;
    cout << "Integration function: " << integral << endl;
    cout << "Interval from " << a << " to " << b << endl;

    double xi;
    for (int i = 0; i < 5; i++)
    {
        xi = ((b + a) / 2) + ((b - a) / 2) * t[i];
        //y = 1;
        y = sin((2 * xi) / (pow(xi, 2)));

        res += y * A[i];
    }
    res *= (b - a) / 2;
    double r = integral - res;
    cout << "Integrand: sin((2 * x) / (pow(x, 2)))" << endl;
    cout << "Gauss: " << res << " | " << "Error: " << r << endl;

    return res;
}

double simpson_def(double a, double b, float x, float y, float res, double integral, int n)
{
    cout << "Enter the number of splits per line: "; cin >> n;

    while (n % 2 != 0)
    {
        cout << "#Error# ~Invalid number~ | Re-enter: "; cin >> n;
    }

    cout << "Interval from " << a << " to " << b << endl;
    float h = (b - a) / n;

    for (int i = 0; i <= n; i++)
    {
        x = a + h * i;
        //y = 1;
        y = sin((2 * x) / (pow(x, 2)));

        if (i % 2 == 0 && i != 0 && i != n) res += y * 2;
        else if (i % 2 != 0 && i != 0 && i != n) res += y * 4;
        else res += y;
    }
    res *= h / 3;
    double r = integral - res;
    cout << "Integrand: sin((2 * x) / (pow(x, 2)))" << endl;
    cout << "Simpson: " << res << " | " << "Error: " << r << endl;
    return res;
}

double trapezoid(double a, double b, float x, float y, float res, double integral, int n)
{
    cout << "Enter the number of splits per line: "; cin >> n;


    cout << "Interval from " << a << " to " << b << endl;
    float h = (b - a) / n;

    for (int i = 0; i <= n; i++)
    {
        x = a + h * i;
        //y = 1;
        y = sin((2 * x) / (pow(x, 2)));
        if (i == 0 || i == n) res += y / 2;
        else res += y;
    }
    res *= h;
    double r = integral - res;
    cout << "Integrand: sin((2 * x) / (pow(x, 2)))" << endl;
    cout << "Trapezoid: " << res << " | " << "Error: " << r << endl;
    return res;
}

double three8(double a, double b, float x, float y, float res, double integral, int n)
{
    cout << "Enter the number of splits per line: "; cin >> n;

    while (n % 3 != 0)
    {
        cout << "#Error# ~Invalid number~ | Re-enter: "; cin >> n;
    }

    cout << "Interval from " << a << " to " << b << endl;
    float h = (b - a) / n;

    for (int i = 0; i <= n; i++)
    {
        x = a + h * i;
        //y = 1;
        y = sin((2 * x) / (pow(x, 2)));

        if (i % 3 == 0 && i != 0 && i != n) res += y * 2;
        else if (i % 3 != 0 && i != 0 && i != n) res += y * 3;
        else res += y;
    }
    res *= (3 * h) / 8;
    double r = integral - res;
    cout << "Integrand: sin((2 * x) / (pow(x, 2)))" << endl;
    cout << "3/8: " << res << " | " << "Error: " << r << endl;
    return res;
}

double def_N2(double a, double b, float x, float y, float res, double integral, int n) //Доработать
{
    int schot = 0;
    double res2 = 0, e = 0;

    cout << "Enter precision: "; cin >> e; cout << endl;
    cout << "Enter the number of splits per line: "; cin >> n;

    while (n % 2 != 0)
    {
        cout << "#Error# ~Invalid number~ | Re-enter: "; cin >> n;
    }

    cout << "Interval from " << a << " to " << b << endl;
    float h = (b - a) / n;

    do
    {
        for (int i = 0; i <= n; i++)
        {
            x = a + h * i;
            //y = 1;
            y = sin((2 * x) / (pow(x, 2)));
            if (i % 2 == 0 && i != 0 && i != n) res += y * 2;
            else if (i % 2 != 0 && i != 0 && i != n) res += y * 4;
            else res += y;
        }
        res *= h / 3;
        n *= 2;
        cout << "2N: " << n << endl;

        for (int i = 0; i <= n; i++)
        {
            x = a + h * i;
            //y = 1;
            y = sin((2 * x) / (pow(x, 2)));
            if (i % 2 == 0 && i != 0 && i != n) res2 += y * 2;
            else if (i % 2 != 0 && i != 0 && i != n) res2 += y * 4;
            else res2 += y;
        }
        res2 *= h / 3;
        schot += 1;

    } while (abs(res - res2) > e);
    cout << "~~~~~~~~" << schot << endl;

    double r = integral - res;
    cout << "Integrand: sin((2 * x) / (pow(x, 2)))" << endl;
    cout << "N: " << res << " | " << "2N: " << res2 << " | " << "Error: " << r << endl;
    return res;
}