#include <iostream>
#include <math.h>
#include <cmath>
using namespace std;

const double pi = 3.1415;
const double e = 2.7182;

typedef double(*pointFunc)(double);

double f1(double x1) {
  return (1/(1+pow(2*x1,0.5)));
}
double f2(double x2) {
	return (pow(e,x2)*sin(x2));
}
double f3(double x3) {
	return (1/(3+2*cos(x3)));
}
double simpson_integral(pointFunc f, double a, double b, int n) {
  const double h = (b-a)/n;
  double k1 = 0, k2 = 0;
  for(int i = 1; i < n; i += 2) {
    k1 += f(a + i*h);
    k2 += f(a + (i+1.)*h);
  }
  return h/3*(f(a) + 4*k1 + 2*k2);
}
int main() {
	setlocale(LC_ALL,"ru");
  double a1=0,a2=0,a3=0, b1=1,b2=pi/4,b3=pi/6, eps;
  double s1,s2,s3,s;
  int n = 1;
  cout << "\nВведите требуемую точность eps = ";
  cin >> eps;
  s1 = simpson_integral(f1, a1, b1, n);
  do {
    s = s1;
    n = 2 * n;
    s1 = simpson_integral(f1, a1, b1, n);
  }
  while (fabs(s1 - s) > eps);

  s2 = simpson_integral(f2, a2, b2, n);
  do {
	  s = s2;
	  n = 2 * n;
	  s2 = simpson_integral(f2, a2, b2, n);
  } while (fabs(s2 - s) > eps);

  s3 = simpson_integral(f3, a3, b3, n);
  do {
	  s = s3;
	  n = 2 * n;
	  s3 = simpson_integral(f3, a3, b3, n);
  } while (fabs(s3 - s) > eps);
  cout << "\n (1/(1+pow(2*x,0.5) Интеграл = " << s1 << " количество разбиений = " << n << endl;
  cout << "\n (pow(e,x)*sin(x)) Интеграл = " << s2 << " количество разбиений =" << n << endl;
  cout << "\n (1/(3+2*cos(x)) Интеграл = " << s3 << " количество разбиений =" << n << endl;
}