Find the surface area of the ellipsoid (x/a)^2 + (y/a)^2 + (z/b)^2 = 1.
If G(u,v) is a map from R2 to R3 that parametrizes the surface, then the area of the surface is equal to the double integral over the domain of G of the norm of the cross product of ∂uG and ∂vG.
The Attempt at a Solution
Well, I can see that we can parametrize the surface with a G whose domain is the circle x^2 + y^2 = a^2. I've tried using polar coordinates, I've tried first transforming it into a sphere and then into polar coordinates, but I just can't seem to get an integral that I can work with.
If someone could perhaps give me a push in the right direction (maybe a parametrization to try out), I would really appreciate it.