In order to evaluate the given integral we first re write it in the form where n is a unit normal vector to the closed surface of the given ellipsoid.
For the purpose,we take --(4)
Then,using (2) and (4),we obtain
Now, by the divergence theorm,V being the volume enclosed by S.
= using (4) and (1)
[Remember that the volume of the ellipsoid is taken in the above step]