integral.cpp

#include <iostream>
#include <cmath>

using namespace std;

inline double f(double x) { return x/(3*x+4)/(3*x+4); }         //  Интегрируемая функция f(x)
inline double F(double x) { return (4/(3*x+4)+log(3*x+4))/9; }  //  Ее первообразная F(x)

double int_rect(double a, double b, double h) {
//  Метод средних прямоугольников
    double r = 0;
    for (double x = a; x <= b-h; x += h)
        r += f(x+h/2);
    r *= h;
    return r;
}

double int_trap(double a, double b, double h) {
//  Метод трапеций
    double r = 0;
    for (double x = a; x <= b-h; x += h)
        r += f(x)+f(x+h);
    r *= h/2;
    return r;
}

double int_simp(double a, double b, double h) {
//  Метод Симпсона
    double r = 0;
    for (double x = a; x <= b-h; x += h)
        r += f(x)+4*f(x+h/2)+f(x+h);
    r *= h/6;
    return r;
}

int main() {
    double a = 0, b = 4, h = 0.01;
    cout << "Rect:\t" << int_rect(a,b,h) << endl;
    cout << "Trap:\t" << int_trap(a,b,h) << endl;
    cout << "Simp:\t" << int_simp(a,b,h) << endl;
    cout << "Real:\t" << F(b) - F(a) << endl;
    cout << "Mist:\t" << fabs(int_simp(a,b,h)-int_simp(a,b,h/2))/15 << endl;
    return 0;
}