Let E be the ellipsoid x^2 + 2xy +5y^ +4z^2 = 1
Find the Volume of E
None, just various integration methods.
The Attempt at a Solution
I know we're not supposed to say 'I don't know where to start' but with this one I really don't. If the best approach is a coordinate change, how would I go about searching for the correct transformation to map this to a sphere?
I tried to solve a similar problem concerning an ellipse (not ellipsoid) and failed to find a substitution. Someone showed me how to solve that problem in cartesian coordinates but that method won't work here.
Can anyone with experience with this type of problem at least tell me whether it's best to search for a substitution or attempt the problem in cartesian? And what my first step in either direction ought to be?