Question

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.

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

yes

Answer 5

okay thx alot =) will try it out

Answer 6

yw