Change of Variables & the Jacobian · Hard problem

Use the substitution $x = 2\rho\sin\phi\cos\theta$, $y = 3\rho\sin\phi\sin\theta$, $z = \rho\cos\phi$ to find the volume of the solid ellipsoid $\dfrac{x^2}{4} + \dfrac{y^2}{9} + z^2 \le 1$.