[tex]\mathbf f(x,y,z)=x^2\sin y\,\mathbf i+x\cos y\,\mathbf j-xz \sin y\,\mathbf k[/tex]
[tex]\implies\nabla\cdot\mathbf f(x,y,z)=2x\sin y-x\sin y-x\sin y=0[/tex]
which means
[tex]\displaystyle\iint_S\mathbf f(x,y,z)\,\mathrm dS=\iiint_R\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=0[/tex]
