temp.cpp

#include <iostream>
#include <cmath>

using namespace std;

inline double f(const double x, const double a, const double b) {
    return (1-cos(b*x))/(x*x)*exp(-a*x);
}

const double pi = acos(-1.0);

int main() {
    const double a = 0.5, b = 0.4;
    const double h = 0.01;
    const int N = 10000000;
    double s = 0.5 + 4*f(h, a, b) + f(2*h, a, b);
    double s2 = 0.5 + f(2*h, a, b);
    double x = 2*h;
    for (int i = 1; i < N; ++i) {
        s2 += f(x, a, b);
        s += f(x, a, b);
        x += h;
        s += 4*f(x, a, b);
        x += h;
        s += f(x, a, b);
        s2 += f(x, a, b);
    }
    cout << s * h / 3 << " ?= " << " ?= " << s2 * h
        << " ?= (formula) " << b*b/(2*a)*(1-exp(-a*pi/b));

    return 0;
}