using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Integral
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = 20;
            double a = 1;
            double b = 2;
            double[] xi = new double[N+1];
            double[] fxi = new double[N + 1];
            double[] rectangle = new double[N + 1];
            double[] trapeze = new double[N + 1];
            int x0 = 0;
            double A = 0;
            double B = 2;
            double dx = (B - A) / N;
            xi = GetXi(xi, dx, x0);
            fxi = GetfXi(xi, a, b);
            rectangle = GetRectangleSolution(fxi, dx);
            trapeze = GetTrapeziumSolution(fxi, dx);
            double sumRectangle = GetSumArray(rectangle);
            double sumTrapeze = GetSumArray(trapeze);
            double calcualtionError = Math.Abs(sumRectangle - sumTrapeze);
            double upperValue = (1 / Math.Pow(a, 3)) * ((a * 2 + b) - 2 * b * Math.Log(Math.Abs(a * 2 + b)) - (Math.Pow(b, 2) / (a * 2 + b)));
            double lowerValue = (1 / Math.Pow(a, 3)) * ((a * 0 + b) - 2 * b * Math.Log(Math.Abs(a * 0 + b)) - (Math.Pow(b, 2) / (a * 0 + b)));
            double exactValue=upperValue - lowerValue;

            ShowResult(xi, fxi, rectangle, trapeze,exactValue);

            Console.ReadKey();

        }

        static double[] GetXi(double[] xi,double dx, int x0)
        {
            for (int i = 0; i < xi.Length; i++)
                xi[i] = x0 + dx * i;

            return xi;
        }
        static double[] GetfXi(double[] xi, double a, double b)
        {
            double[] result = new double[xi.Length];
            for (int i = 0; i < xi.Length; i++)
                result[i] = Math.Pow(xi[i], 2) / Math.Pow((xi[i] * a + b), 2);

            return result;
        }
        static double[] GetRectangleSolution(double[] fxi, double dx)
        {
            double[] result = new double[fxi.Length-1];
            for (int i = 0; i < result.Length; i++)
                result[i] = fxi[i] * dx;

            return result;
        }
        static double GetSumArray(double[] array)
        {
            double result = 0;
            for (int i = 0; i < array.Length; i++)
                result += array[i];

            return result;
        }
        static void ShowArray(double[] array)
        {
            for (int i = 0; i < array.Length; i++)
                Console.WriteLine(" " + array[i]);
        }
        static void ShowResult(double[] xi, double[] fxi, double[] rectangle, double[] trapeze,double exactValue)
        {
            Console.WriteLine("xi\tfxi\trec\ttrape");
            for (int i = 0; i < xi.Length-1; i++)
                Console.WriteLine("{0}\t{1:0.000}\t{2:0.0.000}\t{3:0.000}", xi[i],fxi[i],rectangle[i],trapeze[i]);
            Console.WriteLine();
            Console.WriteLine("Точное значение ={0:0.000}",exactValue);

        }
        static double[] GetTrapeziumSolution(double[] fxi,double dx)
        {
            double[] result = new double[fxi.Length - 1];
            for (int i = 0; i < fxi.Length-1; i++)
                result[i] = (fxi[i] + fxi[i + 1]) / 2 * dx;

            return result;
        }
    }
}