#include<iostream>
#include<iomanip>
#include<cmath>
using namespace std;
void Trapezia(float arr[10], int a, int b, int h, int n);
void Gauss(int b, int a, float h, int n);
int main()
{
    printf("Lab 6\nNumerical integration of functions\nBershadskiy Andrew IS-81\n\n");

    //(cos(x))/x+1;
    float h;
    int a, b, n = 2;
    cout << "(cos(x))/(x+1)" << endl << endl;
    cout << "e = 0,0001" << endl << endl;

    a = 1; b = 3;
    cout << "Boundaries of integration:" << endl;
    cout << "a:" << a << endl << "b:" << b << endl << endl;

    double uravnenie = 1;
    double iterations = 1;
    while(0.0001 <= uravnenie){
        uravnenie = (pow((b-a), 3))/(12*pow(iterations, 2))*0.3101;
        iterations++;
        //
    }
    cout << endl << "Iterations Trapezia:" <<  iterations << endl << endl;


    double uravnenie1 = 1;
    double iterations1 = 1;
    while(0.0001 <= uravnenie1){
        uravnenie1 = (8)/(69120)*(-0.13);
        iterations1++;
        //
    }
    cout << endl << "Iterations Gauss:" <<  iterations1-1 << endl << endl;

    h = (b - a) / n;
    double h1 = (b - a) / iterations;
    cout << "h = (b - a) / n" << endl << "h = " << h1 << endl << endl;

    float arr[10] = { 0 };
    Trapezia(arr, a, b, h, n);
    Gauss(b, a, h, n);
    getchar();
    return 0;
}
void Trapezia(float arr[10], int a, int b, int h, int n)
{
    float S = 0, S1 = 0, S2 = 0;
    for (int i = 0; i <= n; i++)
    {
        arr[0] = a;
        if (i != 0)
        {
            arr[i] = arr[i - 1] + h;
        }
    }
    S1 = ((cos(a) / (a + 1)) + (cos(b) / (b + 1)));
    for (int i = 1; i < n; i++)
    {
        S2 += cos(arr[i]) / (arr[i] + 1);
    }
    S = (S1 + 2 * S2) * 1 / 2;
    cout << "Result with method of Trapezoid = " << S << endl;
}
void Gauss(int b, int a, float h, int n)
{
    float arr1[2] = { -0.5735,0.5735 };
    float newarr1[2] = { 0 };
    float arr2[2] = { 1,1 };
    float rez = 0;
    for (int i = 0; i < n; i++)
    {
        newarr1[i] = ((b + a) / 2) + ((b - a) / 2)*arr1[i];
    }
    for (int i = 0; i < n; i++)
    {
        rez += arr2[i] * cos(newarr1[i]) / (newarr1[i] + 1);
    }
    rez = rez*((b - a) / 2);
    cout << "Result with Gauss = " << rez << endl;

}