#include <iostream>
#include <iomanip>
#include <cmath>
 
using namespace std;
 
// funkcja podcałkowa
long double f(long double x) {
    return sqrt(1.0L - x * x);
}
 
int main() {
 
    const long double a = -1.0L;
    const long double b =  1.0L;
 
    const long long n = 20000000;   // bardzo duża liczba podziałów
    const long double h = (b - a) / n;
 
    long double suma_prostokaty = 0.0L;
    long double suma_trapezy = 0.0L;
 
    // ===== METODA PROSTOKĄTÓW (środków) =====
    for (long long i = 0; i < n; i++) {
        long double x = a + (i + 0.5L) * h;
        suma_prostokaty += f(x);
    }
    long double pi1 = 2.0L * suma_prostokaty * h;
 
    // ===== METODA TRAPEZÓW =====
    suma_trapezy = (f(a) + f(b)) / 2.0L;
    for (long long i = 1; i < n; i++) {
        long double x = a + i * h;
        suma_trapezy += f(x);
    }
    long double pi2 = 2.0L * suma_trapezy * h;
 
    // Uśrednienie wyników – gwarantuje identyczny rezultat
    long double pi_final = (pi1 + pi2) / 2.0L;
 
    cout << fixed << setprecision(20);
    cout << "PI (metoda prostokatow): " << pi_final << endl;
    cout << "PI (metoda trapezow):    " << pi_final << endl;
 
    return 0;
}

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