(This was a question from my calculus final this semester.)
Find the volume bounded by the surface and the first octant.
Using the change of variables the Jacobian of the transformation is .
So now, I tried to find volume by calculating the triple integral over the constraints .
What I'm not sure about is the bounds of the regions; here's what I have:
For the original region E, , and for the transformed region T(E), .
Is that right? I'm confused by the positive/negative signs that result from squaring and square roots.