Make the change of variables , for which the Jacobian is
= = 24
The ellipsoid is now described by , and the density by .
The total mass is then given by the triple integral
where is now the interior of the unit sphere centered at the origin , and is the element of volume: 24 times the appropriate triple of differentials .
Next, change to spherical coordinates according to the transformation laws
The density is then , so the total mass is given by the iterated integral
=