## anonymous 4 years ago Evaluate $\int\limits_{}^{}\int\limits_{}^{}\int\limits_{E}^{}2xdV$ where E is the region under the plane 2x+3y+z=6 that lies in the first octant.

1. anonymous

i know when z=0, i got the x-y plane graph |dw:1342605711765:dw| but how to know the limit of integration for dz?

2. anonymous

$\int _0^3\int _0^{\frac{1}{3} (6-3 x)}\int _0^{-2 x-3 y+6}2 xdzdydx=\frac{9}{4}$

3. anonymous

owh so we just let the whole equation be in terms of z to integrate z?

4. anonymous

yes

5. anonymous

okay thx alot =) will try it out

6. anonymous

yw