Suppose I have a integral $$ I = \iint \vec{F}\cdot\vec{ds}$$ for $$ \vec{F} = 2xy\vec{i} +yz\vec{j} + xz \vec{k}$$
in the region where $x = 0 , y=0, z = 0, y = 3, x+2z = 6.$
I know that I can use Gauss's divergence theorem which would make this problem pretty simple that is $$\iint \vec{F}\cdot\vec{ds} = \iiint \nabla\cdot\vec{F}\,dV$$
which makes my integral
$$ \iiint (2xy + yz + xz)\,dx\,dy\,dz$$
but what would be it's limits? I know that will range from $ y = 0 \rightarrow 3$ but what about $x$ and $z$?