I found this exercise while exercising for the exam:
Let $T$ $\subset$ $R^2$ be the triangle with these vertices $(0,0), (2,0), (0,1)$ and let $\Omega$ be the surface defined like this:
$\Omega$ = {$(x,y,z) \in R^3 : z^2 - x^2 - y^2 = 0, z > 0, (x,y) \in T$}
Evaluate $\iint_{\Omega}x^2 y dS $
I'm having a hard time solving it because it confounds me... I can't seem to "visualize" the situation. What's exactly the role of the triangular region, where am I going to have to use that region when solving the integral?
Could you help me visualize the problem in some way?