monte_carlo

import numpy as np
from math import cos, pi


def MonteCarlo_method(f, g, x0, x1, y0, y1, n):
    x = np.random.uniform(x0, x1, n)
    y = np.random.uniform(y0, y1, n)
    f_avg = 0
    amount_inside = 0
    for i in range(len(x)):
        for j in range(len(y)):
            if g(x[i], y[j]):
                amount_inside += 1
                f_avg += f(x[i], y[j])

    f_avg = f_avg / float(amount_inside)
    area = amount_inside / float(n**2) * (x1 - x0) * (y1 - y0)
    return area * f_avg