package numeric;

import java.util.function.DoubleFunction;

public class SimpsonIntegration {

public static double integrate(DoubleFunction<Double> f, double a, double b) {

double eps = 1e-10;

double m = (a + b) / 2;

double am = simpsonIntegration(f, a, m);

double mb = simpsonIntegration(f, m, b);

double ab = simpsonIntegration(f, a, b);

if (Math.abs(am + mb - ab) < eps)

return ab;

return integrate(f, a, m) + integrate(f, m, b);

}

static double simpsonIntegration(DoubleFunction<Double> f, double a, double b) {

return (f.apply(a) + 4 * f.apply((a + b) / 2) + f.apply(b)) * (b - a) / 6;

}

// Usage example

public static void main(String[] args) {

System.out.println(integrate(x -> Math.sin(x), 0, Math.PI / 2));

}

}