Question

Evaluate

Answer 1

I got 1/3 ??

Answer 2

ask wolfram

Answer 3

http://www.wolframalpha.com/input/?i=%5Cint_0%5E2+%5Cint_0%5E%282-y%29+%5Cint_0%5E%28sqrt%281-y%5E2%29%29+z+dz+dx+dy

Answer 4

wolfram nice.D

Answer 5

I prefer not to respond with "right" or "wrong" when asked to confirm someone else's answer. On the other hand, were you to show how you got your answer, there'd be plenty on which to comment.

I'd strongly suggest that you draw the region of integration in the xy plane first. While not strictly necessary, drawing this 3-D shape might also help you to visualize it and figure out what to do next.

Answer 6

One thing that might make your work easier would be to notice that you are asked to integrate first with respect to z. The integral from 0 to \[\sqrt{1-y^2)} ~of ~dz ~is ~what?\]

Answer 7

Note that we are actually integrating z dz, not just dz. My bad.

Answer 8

yeah simplifies nicely :)