a = 3
b = 5

x = a * np.cos(t)
y = b * np.sin(t)

dx = -a * np.sin(t)
dy = b * np.cos(t)
dl = np.sqrt(dx**2 + dy**2)
L = (dl*dt).sum()

w = 1 + np.pi/(2*t)
x = a * np.sin(w*t)
y = b * np.sin(t)

dw = -np.pi/(2*t**2)
dx = a * np.cos(w*t) * (w + t * dw)
dy = b * np.cos(t)

dl = np.sqrt(dx**2 + dy**2)
L2 = (dl*dt).sum()