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

using namespace std;

const double lowestLimits[3] = {0, 0, -2};
const double highestLimits[3] = {1.7, 2, -1.2};

double (*integralFunctions[3])(double, double) = {
    [](double x, double step)
    { return 0.5 * step * (x * atan(x) + (x + step) * atan(x + step)); },
    [](double x, double step)
    { return 0.5 * step * (1 / (1 + sqrt(x)) + (1 / (1 + sqrt(x + step)))); },
    [](double x, double step)
    { return 0.5 * step * (2 / (1 - 4 * x) + (2 / (1 - 4 * (x + step)))); }
};

double integral(int n, int indexOfIntegral)
{
    double step = abs(highestLimits[indexOfIntegral] - lowestLimits[indexOfIntegral]) / n;
    double result = 0, sum = 0, x = lowestLimits[indexOfIntegral];
    for (int i = 0; i < n; i++)
    {
        sum = (integralFunctions[indexOfIntegral](x, step));
        x += step;
        result += sum;
    }
    return result;
}

int main()
{
    double acc;
    cout << "Input accuracy: ";
    cin >> acc;
    cout << endl;

    for (int i = 0; i < 3; i++)
    {
        int n = 1;
        double previousResult, currentResult = integral(n, i);
        do
        {
            ++n;
            previousResult = currentResult;
            currentResult = integral(n, i);
        } while (n < INT_MAX && !(abs(currentResult - previousResult) <= acc));

        cout << "### - " << i + 1 << endl;
        cout << "amount of trapezoids = " << n << endl;
        cout << "integral of n = " << previousResult << endl;
        cout << "integral of n + 1 = " << currentResult << endl;
        cout << "delta = " << abs(currentResult - previousResult) << endl
             << endl;
    }

    return 0;
}