#define _USE_MATH_DEFINES
#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <math.h>

using namespace std;

int count_r = 9;
double eps = 0.001;
double a = 0;//1kek
double b = 0.9;//2

double f(double x) {
	//return x*x*log(x);
	//return 1/(x*x-1);
	return x*asin(x);
}

double f1(double x) {
	return asin(x) + x/sqrt(1-x*x);
}

double f2(double x) {
	//return (6 * x*x + 2) / (pow(x*x - 1, 3));
	return -(x*x - 2.0) / pow((1 - x*x), 1.5);
}

int main() {
	system("color F2");
	ifstream fin("in.txt");
	ofstream fout("res.txt");
	double x2 = b;
	double M = abs(f2(x2));
	{

		cout << "M = " << M << endl;
		double h1 = sqrt(eps * 12 / M / abs(b - a));
		double h2 = sqrt(eps * 12 / M / abs(b - a));

		double res1 = 0, res2 = 0;

		{
			cout << "h1 < " << h1 << endl;


			double n = (b - a) / h1;
			cout << "n1 ~= " << n << endl;
			while ((int)n % 4 != 0) {
				n += 1;
			}
			n = (int(n));
			cout << "n1 = " << n << endl;
			//n = 32;

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

			//cout << "~ = " << (f(a) + f(b))*h / 2 << endl;

			for (int i = 1; i < n; i++) {
				res1 += f(a + h1 * i);
			}

			res1 += f(a) / 2 + f(b) / 2;
			res1 *= h1;
		}
		cout << "------------------------------------" << endl;
		{
			h2 = 2 * h1;
			cout << "h < " << h2 << endl;

			double n = (b - a) / h2;
			cout << "n2 ~= " << n << endl;
			/*while ((int)n % 4 != 0) {
				n += 1;
			}*/
			n = (int(n));
			cout << "n2 = " << n << endl;
			//n = 32;

			h2 = (b - a) / n;
			cout << "h2 = " << h2 << endl;

			//cout << "~ = " << (f(a) + f(b))*h / 2 << endl;

			for (int i = 1; i < n; i++) {
				res2 += f(a + h2 * i);
			}
			res2 += f(a) / 2 + f(b) / 2;
			res2 *= h2;
		}
		cout << "------------------------------------" << endl;

		cout << "res1 = " << res1 << "  " << "res2 = " << res2 << endl;
		cout << "delta = " << (res2 - res1) / 3 << '\n';

	}



	{
		double h1 = sqrt(eps * 12 / M / abs(b - a));
		double h2 = sqrt(eps * 12 / M / abs(b - a));

		double res1 = 0, res2 = 0;

		cout << "------------------------------------" << endl;
		{
			cout << "h1 < " << h1 << endl;

			double n = (b - a) / h1;
			cout << "n1 ~= " << n << endl;
			while ((int)n % 4 != 0) {
				n += 1;
			}
			n = (int(n));
			cout << "n1 = " << n << endl;
			//n = 32;

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

			//cout << "~ = " << (f(a) + f(b))*h / 2 << endl;
			//int m = n / 2;
			for (int i = 1; i < n; i++) {
				if (i%2 == 0) res1 += f(a + h1 * i);
				else res1 += 2*f(a + h1 * i);
			}
			res1 += f(a) / 2 + f(b) / 2;
			res1 *= 2*h1/3;
		}
		cout << "------------------------------------" << endl;
		{
			h2 = 2 * h1;
			cout << "h < " << h2 << endl;


			double n = (b - a) / h2;
			cout << "n2 ~= " << n << endl;
			/*while ((int)n % 4 != 0) {
			n += 1;
			}*/
			n = (int(n));
			cout << "n2 = " << n << endl;
			//n = 32;

			h2 = (b - a) / n;
			cout << "h2 = " << h2 << endl;

			//cout << "~ = " << (f(a) + f(b))*h / 2 << endl;

			for (int i = 1; i < n; i++) {
				if (i % 2 == 0) res2 += f(a + h2 * i);
				else res2 += 2 * f(a + h2 * i);
			}
			res2 += f(a) / 2 + f(b) / 2;
			res2 *= 2 * h2 / 3;
		}
		cout << "------------------------------------" << endl;

		cout << "res1 = " << res1 << "  " << "res2 = " << res2 << endl;
		cout << "delta = " << (res2 - res1) / 3 << '\n';
	}
	system("pause");
	return 0;
}