using System;

public class Program

{

    public static double Function(double x)

    {

        return (1 - Math.Log(x, Math.E)) / (2 + Math.Log(1 + x * x, Math.E));

    }

    public static double LeftRect(double a, double b, int n)

    {

        double step = Math.Abs(a - b) / n;

        double sum = 0.0;

        for(int i = 0; i < n - 1; ++i)  

            sum += Function(a + step * i);  

        return step * sum;

    }

    public static double LeftRectIter(double a, double b, double epsilon)

    {

        int n = 10;

        double previousResult = -9999;

        double result = -999;

        while(Math.Abs(result - previousResult) > epsilon)

        {

            if(result > 0)

            {

                previousResult = result;

                result = LeftRect(a, b, n);

            }

            else

                result = LeftRect(a, b, n);

            n *= 2;

        }

        return result;

    }

    public static double RightRect(double a, double b, int n)

    {

        double step = Math.Abs(a - b) / n;

        double sum = 0.0;

        for(int i = 1; i < n; ++i)  

            sum += Function(a + step * i);  

        return step * sum;

    }

    public static double RightRectIter(double a, double b, double epsilon)

    {

        int n = 10;

        double previousResult = -9999;

        double result = -999;

        while(Math.Abs(result - previousResult) > epsilon)

        {

            if(result > 0)

            {

                previousResult = result;

                result = RightRect(a, b, n);

            }

            else

                result = RightRect(a, b, n);

            n *= 2;

        }

        return result;

    }

    public static double MidRect(double a, double b, int n)

    {

        double step = Math.Abs(a - b) / n;

        double sum = 0.0;

        for(int i = 0; i < n - 1; ++i)  

        {

            double fun =  ( Function(a + step * i) +  Function(a + step * (i + 1))) / 2;    

            sum += fun;

        }

        return step * sum;

    }

    public static double MidRectIter(double a, double b, double epsilon)

    {

        int n = 10;

        double previousResult = -9999;

        double result = -999;

        while(Math.Abs(result - previousResult) > epsilon)

        {

            if(result > 0)

            {

                previousResult = result;

                result = MidRect(a, b, n);

            }

            else

                result = MidRect(a, b, n);

            n *= 2;

        }

        return result;

    }

    public static double Trap(double a, double b, int n)

    {

        double step = Math.Abs(a - b) / n;

        double sum = 0.0;

        for(int i = 0; i < n - 1; ++i)  

        {

            double x = a + step * i;

            double o = Function(x) + Function(x + step);

            sum += step * 0.5 * o;

        }

        return sum;

    }

    public static double TrapIter(double a, double b, double epsilon)

    {

        int n = 10;

        double previousResult = -9999;

        double result = -999;

        while(Math.Abs(result - previousResult) > epsilon)

        {

            if(result > 0)

            {

                previousResult = result;

                result = Trap(a, b, n);

            }

            else

                result = Trap(a, b, n);

            n *= 2;

        }

        return result;

    }

    public static void Main()

    {

        double eps = 1E-5;

        Console.WriteLine("Метод левых прямоугольников: " + LeftRectIter(1, 2, eps));

        Console.WriteLine("Метод правых прямоугольников: " + RightRectIter(1, 2, eps));

        Console.WriteLine("Метод средних прямоугольников: " + MidRectIter(1, 2, eps));

        Console.WriteLine("Метод трапеций: " + TrapIter(1, 2, eps));

    }

}