#include <iostream>
#include <iomanip>
#include <cmath>



double f1(double x)
{
	return x;
}
double f2(double x)
{
	return (sin(22 * x));
}
double f3(double x)
{
	return (x * x * x * x);

}
double f4(double x)
{
	return (atan(x));
}

double zn1(double a, double b)
{
	return ((b * b - a * a) / 2.0);
}

double zn2(double a, double b)
{
	return((cos(a * 22.0) - cos(b * 22.0)) / 22.0);
}
double zn3(double a, double b)
{
	return ((b * b * b * b * b - a * a * a * a * a) / 5.0);
}
double zn4(double a, double b)
{
	return (b * atan(b) - a * atan(a) - (log(b * b + 1) - log(a * a + 1)) / 2.0);
}


typedef double (*TPF)(double);

double IntWorkRect(TPF f, double a, double b, double dx) {
	double s = 0;
	for (double x = a; x < b; x += dx) {
		s += f(x + dx / 2);
	}
	return s * dx;
}

double IntRect(TPF f, double a, double b, double eps, int& n) {
	double dx = (b - a) / 2;
	double s1 = IntWorkRect(f, a, b, dx);
	double s2 = IntWorkRect(f, a, b, dx / 2);
	while (abs(s1 - s2) > eps) {
		dx /= 2;
		s1 = s2;
		s2 = IntWorkRect(f, a, b, dx / 2);
		n *= 2;
	}
	return s2;
}


double IntWorkTrap(TPF f, double a, double b, double dx) {
	double s = 0;
	for (double x = a; x < b; x += dx) {
		s += (f(x) + f(x + dx)) / 2;
	}
	s *= dx;
	return s ;
}

double IntTrap(TPF f, double a, double b, double eps, int& n) {
	double dx = (b - a) / 2;
	double s1 = IntWorkTrap(f, a, b, dx);
	double s2 = IntWorkTrap(f, a, b, dx / 2);
	while (abs(s1 - s2) > eps) {
		dx /= 2;
		s1 = s2;
		s2 = IntWorkTrap(f, a, b, dx / 2);
		n *= 2;
	}
	return s2;
}
 #include <iostream>
#include <iomanip>
#include <cmath>
#include "прототипы.h"
using namespace std;

struct I_print {	//данные для печати результатов интегрирования
	const char* name;//название функции
	double sum;	//значение интегральной суммы
	double zn;	//точное значение интеграла
	int n;	//число разбиений области интегрирования
			//при котором достигнута требуемая точность
};

void print(I_print h[])
{
	const int m = 4;//число столбцов таблицы
	int wn[m] = { 20,20,20,20 };//ширина столбцов таблицы
	 const char* title[m] = {"Function","Integral","IntSum","N "};
	int size[m];
	for (int i = 0; i < m; i++)
		size[i] = strlen(title[i]);
	//шапка таблицы
	cout << char(218) << setfill(char(196));
	for (int j = 0; j < m - 1; j++)
		cout << setw(wn[j]) << char(194);
	cout << setw(wn[m - 1]) << char(191) << endl;

	cout << char(179);
	for (int j = 0; j < m; j++)
		cout << setw((wn[j] - size[j]) / 2) << setfill(' ') << ' ' << title[j]
		<< setw((wn[j] - size[j]) / 2) << char(179);
	cout << endl;
	for (int i = 0; i < 4; i++)
	{//заполнение таблицы
		cout << char(195) << fixed;
		for (int j = 0; j < m - 1; j++)
			cout << setfill(char(196)) << setw(wn[j]) << char(197);
		cout << setw(wn[m - 1]) << char(180) << setfill(' ') << endl;

		cout << char(179) << setw((wn[0] - strlen(h[i].name)) / 2) << ' ' << h[i].name
			<< setw((wn[0] - strlen(h[i].name)) / 2) << char(179);
		cout << setw(wn[1] - 1) << setprecision(10) << h[i].zn << char(179)
			<< setw(wn[2] - 1) << h[i].sum << setprecision(6) << char(179)
			<< setw(wn[3] - 1) << h[i].n << char(179) << endl;
	}
	//низ таблицы
	cout << char(192) << setfill(char(196));
	for (int j = 0; j < m - 1; j++)
		cout << setw(wn[j]) << char(193);
	cout << setw(wn[m - 1]) << char(217) << setfill(' ') << endl;
}


int main()
{

	double a = -1;
	double b = 3;
	cout << "from  " << a << " to " << b << endl;
	int n = 8;
	double eps = 0.01;
	double (*F[])(double) = { f1, f2, f3, f4 };

	I_print m[4];

	m[0].zn = zn1(a, b);
	m[1].zn = zn2(a, b);
	m[2].zn = zn3(a, b);
	m[3].zn = zn4(a, b);

	m[0].name = "y = x ";
	m[1].name = "y = sin(22x)";
	m[2].name = "y = x^4 ";
	m[3].name = "y = arctan(x) ";
	cout << "Rectangle" << endl;
	while (eps > 0.000001)
	{
		cout << eps << endl;
		for (int i = 0; i < 4; i++)
		{
			m[i].sum = IntRect(F[i], a, b, eps, n);
			m[i].n = n;
			n = 1;
		}
		print(m);
		eps /= 10;
	}
	I_print h[4];

	h[0].zn = zn1(a, b);
	h[1].zn = zn2(a, b);
	h[2].zn = zn3(a, b);
	h[3].zn = zn4(a, b);

	h[0].name = "y = x ";
	h[1].name = "y = sin(22x)";
	h[2].name = "y = x^4 ";
	h[3].name = "y = arctan(x) ";
	eps = 0.01;
	cout << "Trapeze" << endl;
	while (eps > 0.000001)
	{
		cout << eps << endl;
		for (int i = 0; i < 4; i++)
		{
			h[i].sum = IntTrap(F[i], a, b, eps, n);
			h[i].n = n;
			n = 1;
		}
		print(h);
		eps /= 10;
	}


	return 0;
}