Change of Variables & the Jacobian · Superchallenge problem

Find the $4$-dimensional volume of the unit ball $x_1^2 + x_2^2 + x_3^2 + x_4^2 \le 1$ in $\mathbb{R}^4$, using the double polar coordinates $x_1 = r\cos\alpha$, $x_2 = r\sin\alpha$, $x_3 = s\cos\beta$, $x_4 = s\sin\beta$.