[tex]\mathbf f(x,y,z)=3x\,\mathbf i+xy\,\mathbf j+4xz\,\mathbf k[/tex]
[tex]\implies\nabla\cdot\mathbf f(x,y,z)=3+x+4x=3+5x[/tex]
[tex]\displaystyle\iint_{\partial E}\mathbf f(x,y,z)\,\mathrm dS=\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV[/tex]
[tex]=\displaystyle\int_{z=0}^{z=3}\int_{y=0}^{y=3}\int_{x=0}^{x=3}(3+5x)\,\mathrm dx\,\mathrm dy\,\mathrm dz[/tex]
[tex]=\displaystyle9\int_0^3(3+5x)\,\mathrm dx[/tex]
[tex]=\dfrac{567}2[/tex]
