Using Gauss theorem I want to calculate $\iint_{\Sigma}f\cdot N\ dA$ where $\Sigma$ is the closed boundary surface of the bounded space that is defined by the surfaces with equations $x=y^2$, $x=9$, $z=0$, $x=z$, and $f(x,y,z)=(3x-5y, 4z-2y, 8yz)$ and the perpendicular vectors $N$ direct to the outside of the space.
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From Gauss theorem we have that $$\iint_{\Sigma}f\cdot N\ dA=\iiint_{\Omega}\nabla \cdot f\ dV$$
We have that $$\nabla \cdot f=\frac{\partial{(3x-5y)}}{ \partial{x}}+\frac{\partial{(4z-2y)}}{ \partial{y}}+\frac{\partial{(8yz)}}{ \partial{z}}=3+(-2)+8y=1+8y$$
It is left to get the boundaries for the right integral.
Do we get $\Omega=\{(x,y,z) \mid 0\leq x\leq 9, -\sqrt{x}\leq y\leq \sqrt{x}, 0\leq z\leq x\}$ ?