[tex]\nabla\cdot\mathbf f(x,y,z)=\dfrac{\partial(2x)}{\partial x}+\dfrac{\partial(xy)}{\partial y}+\dfrac{\partial(3xz)}{\partial z}=2+x+3x=4x+2[/tex]
The flux across [tex]\partial\mathcal E[/tex] (boundary of [tex]\mathcal E[/tex]) is
[tex]\displaystyle\iint_{\partial\mathcal E}\mathbf f(x,y,z)\cdot\mathrm d\mathbf S=\iiint_{\mathcal E}(4x+2)\,\mathrm dV[/tex]
[tex]=\displaystyle\int_{z=0}^{z=2}\int_{y=0}^{y=2}\int_{x=0}^{x=2}(4x+2)\,\mathrm dx\,\mathrm dy\,\mathrm dz=48[/tex]
