#include <stdio.h>
#include <math.h>

double function(double theta, double k) {
    return sqrt(1.0 - pow(k, 2) * pow(sin(theta), 2));
}

int main() {
    double k = 1.0 / sqrt(2.0);
    int n = 1000000; // Anzahl der Schritte
    double a = 0.0, b = M_PI_2;
    double h = (b - a) / n;
    double integral = 0.5 * (function(a, k) + function(b, k));

    for (int i = 1; i < n; i++) {
        integral += function(a + i * h, k);
    }
    
    double E = integral * h;
    double s = 8.0 * sqrt(2.0) * E;

    printf("E(k) = %.10f\n", E);
    printf("Bogenlaenge s = %.10f\n", s);
    return 0;
}