import numpy as np

def fun_integrand(x):
    r = 0.5*x
    return np.pi*r**2

x_a = 0
x_b = 4
dx = 0.01
N = int((x_b - x_a)/dx + 1)
x_array = np.linspace(x_a, x_b, N)
k_array = np.arange(0, N)

y_array = fun_integrand(x_array)
V_num = (np.sum((y_array[0:-1] + y_array[1:]))/2)*dx

print('Volum beregnet som numerisk integral =', V_num)
print('Eksakt volum = ', 16*np.pi/3)