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

using namespace std;


double func1(double x)
{
    double Y = (sqrt(0.6*x + 1.5)) / (2*x + sqrt(x*x + 3));
    return Y;
}

double func2(double x)
{
    double Y = 1 / sqrt(x*x + 0.6);
    return Y;
}

double func3(double x)
{
    double Y = (sin(0.8 * pow(x,2) + 0.3)) / (0.7 + cos(1.2*x + 0.3));
    return Y;
}

double func4(double x)
{
    double Y = (pow(x, 2) * log(x));
    return Y;
}


/* ==========================
 Fucntions Of Solving Method
 ========================== */

double meth1(double a, double b, int n)
{
    double sum = 0, h, I;

    h = (b - a) / n;

    for(int i = 0; i <= (n - 1); i++)
    {
        sum += func1((a + i*h));
    }

    I = h * sum;
    return I;
}

double meth2(double a, double b, int n)
{
    double sum = 0, h, I;

    h = (b - a) / n;

    for(int i = 1; i <= n; i++)
    {
        sum += func2((a + i*h));
    }

    I = h * sum;
    return I;
}

double meth3(double a, double b, int n)
{
    double sum = 0, h, I;

    h = (b - a) / n;

    for(int i = 0; i <= (n - 1); i++)
    {
        sum += func3((a + i*h + h/2));
    }

    I = h * sum;
    return I;
}

double meth4(double a, double b, int n)
{
    double sum = 0, h, I;

    h = (b - a) / n;
    sum = (func4(a) + func4(a + n*h)) / 2;

    for(int i = 1; i <= n; i++)
    {
        sum += func4((a + i*h));
    }

    I = h * sum;
    return I;
}



/* ==========================
 Fucntions Of Accuracy
 ========================== */

double accuracy1(double a, double b, int n){
    double Eps;
    cout << "Введите точность: ";
    cin >> Eps;

    for(int i = 0; i < n; i++){
        if(abs(meth1(a, b, n + 1) - meth1(a, b, n)) <= Eps)
            return meth1(a, b, n);
        else n++;
    }
    return 0;
}

double accuracy2(double a, double b, int n)
{
    double Eps;
    cout << "Введите точность: ";
    cin >> Eps;

    for(int i = 0; i < n; i++){
        if(abs(meth2(a, b, n + 1) - meth2(a, b, n)) <= Eps)
            return meth2(a, b, n);
        else n++;
    }
    return 0;
}

double accuracy3(double a, double b, int n)
{
    double Eps;
    cout << "Введите точность: ";
    cin >> Eps;

    for(int i = 0; i < n; i++){
        if(abs(meth3(a, b, n + 1) - meth3(a, b, n)) <= Eps)
            return meth3(a, b, n);
        else n++;
    }
    return 0;
}

double accuracy4(double a, double b, int n)
{
    double Eps;
    cout << "Введите точность: ";
    cin >> Eps;

    for(int i = 0; i < n; i++){
        if(abs(meth4(a, b, n + 1) - meth4(a, b, n)) <= Eps)
            return meth4(a, b, n);
        else n++;
    }
    return 0;
}


int main()
{
    double a, b;
    int n = 1;



    /* ==========================
     First Integral
     ========================== */

    cout << "Введите начало промежутка: ";
    cin >> a;

    while(a <= 0){
        cout << "Введите начало промежутка > 0: ";
        cin >> a;
    }

    cout << "\n";

    cout << "Введите конец промежутка: ";
    cin >> b;

    while(b <= 0){
        cout << "Введите конец промежутка > 0: ";
        cin >> b;
    }



    cout << "Первый интеграл равен, " << accuracy1(a, b, n) << endl;
    // End First




    cout << "\n\n";





    /* ==========================
     Second Integral
     ========================== */

    cout << "Введите a: ";
    cin >> a;

    while(a <= 0){
        cout << "Введите a > 0: ";
        cin >> a;
    }

    cout << "\n";

    cout << "Введите b: ";
    cin >> b;

    while(b <= 0){
        cout << "Введите b > 0: ";
        cin >> b;
    }

    cout << "Второй интеграл равен, " << accuracy2(a, b, n) << endl;

    // End Second




    cout << "\n\n";




    /* ==========================
     Third Integral
     ========================== */

    cout << "Введите a: ";
    cin >> a;

    while(a <= 0){
        cout << "Введите a > 0: ";
        cin >> a;
    }

    cout << "\n";

    cout << "Введите b: ";
    cin >> b;

    while(b <= 0){
        cout << "Введите b > 0: ";
        cin >> b;
    }

    cout << "Третий интеграл равен, " << accuracy3(a, b, n) << endl;

    // End Third




    cout << "\n\n";




    /* ==========================
     Fourth Integral
     ========================== */

    cout << "Введите a: ";
    cin >> a;

    while(a <= 0){
        cout << "Введите a > 0: ";
        cin >> a;
    }

    cout << "\n";

    cout << "Введите b: ";
    cin >> b;

    while(b <= 0){
        cout << "Введите b > 0: ";
        cin >> b;
    }

    cout << "Четвертый интеграл равен, " << accuracy4(a, b, n) << endl;

    // End Fourth

    return 0;
}