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  1. #include <iostream>
  2. #include <cmath>
  3. #include <iomanip>
  4. using namespace std;
  5.  
  6. // f(x) = sqrt(1 - x^2)
  7. double f(double x) {
  8.     return sqrt(1.0 - x * x);
  9. }
  10.  
  11. // Metoda prostokątów (środek przedziału)
  12. double metodaProstokatow(double a, double b, int n) {
  13.     double h = (b - a) / n;
  14.     double suma = 0.0;
  15.  
  16.     for(int i = 0; i < n; i++) {
  17.         double x = a + (i + 0.5) * h;
  18.         suma += f(x);
  19.     }
  20.  
  21.     return 2.0 * h * suma;
  22. }
  23.  
  24. // Metoda trapezów
  25. double metodaTrapezow(double a, double b, int n) {
  26.     double h = (b - a) / n;
  27.     double suma = 0.5 * (f(a) + f(b));
  28.  
  29.     for(int i = 1; i < n; i++) {
  30.         double x = a + i * h;
  31.         suma += f(x);
  32.     }
  33.  
  34.     return 2.0 * h * suma;
  35. }
  36.  
  37. int main() {
  38.     double a = -1.0;
  39.     double b = 1.0;
  40.     int n = 1000000; // liczba podprzedziałów
  41.  
  42.     double piProstokaty = metodaProstokatow(a, b, n);
  43.     double piTrapezy = metodaTrapezow(a, b, n);
  44.  
  45.     cout << fixed << setprecision(20);
  46.     cout << "π (metoda prostokatow): " << piProstokaty << endl;
  47.     cout << "π (metoda trapezow):    " << piTrapezy << endl;
  48.     cout << "π (wartosc dokladna):   " << acos(-1) << endl;
  49.  
  50.     return 0;
  51. }
Success #stdin #stdout 0.02s 5324KB
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stdin
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Standard input is empty
stdout
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π (metoda prostokatow): 3.14159265456397474026
π (metoda trapezow):    3.14159265026386957942
π (wartosc dokladna):   3.14159265358979311600
https://ideone.com/ZFCd05
language:
C++ (gcc 8.3)
created:
1 day ago
visibility:
public

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