I want to calculate vector field:
$$\mathbf{F} = ({3\cdot x^3\cdot y^2+3})\mathbf{i}+({\frac{y^2+2\cdot x}{3}})\mathbf{j}+({3\cdot y\cdot z^3+3})\mathbf{k}$$
flux from the box which coordinates are $(0,1,0)$ and $(2,2,1)$ and the faces are parallel to the coordinate planes.
So
$$\iiint_V\frac{\delta F_x}{\delta x}+\frac{\delta F_y}{\delta y}+\frac{\delta F_z}{\delta z}\,dV=\int_0^2\int_1^2\int_0^19x^2y+\frac{2y}{3}+9z^2y\,dx\,dy\,dz=52$$
$52$ is not correct answer. I don't know where I have done mistake.
We have
$$\iiint_V\frac{\delta F_x}{\delta x}+\frac{\delta F_y}{\delta y}+\frac{\delta F_z}{\delta z}\,dV=\int_0^2\int_1^2\int_0^1 \color{green}{9x^2y^2}+\frac{2y}{3}+9z^2y\color{red}{\,dz}\,dy\color{red}{\,dx}=67$$