Triple Integrals: Finding Limits Without Sketching

[roam]

Homework Statement

Here is a solved problem:

[PLAIN]http://img3.imageshack.us/img3/6948/97765276.gif

In part (e), they formulated the triple integral using the limits of integration they found by sketching the region. Is there a way we can find the limits of integration without sketching the region? To me, sketching this graph looks complicated, so I'm wondering if we can determine the limits for the iterated integral by just using the given equations...

The Attempt at a Solution

I appreciate any help.

 

[radou]

Why would sketching a plane be complicated? 3 points are enough to determine a plane. So, for example, if you have some plane given with x + y + z = C, set x = y = 0 and find z, then set y = z = 0, and find x, and set x = z = 0, and find y.