Evaluate $\iint_{\partial W} F \cdot dS$

Bu Gauss's theorem 

\[\iint_{\partial W} D\cdot dS=\iiint_{W} \nabla \cdot F dV=\iiint_{W} x dV\]
Using cyllindrical coordinates we have
\[=\int_{0}^{2\pi}\int_0^{1} \int_{r^2}^{1}r \cos \theta dz dr d\theta\]
\[=\int_0^{2\pi}\cos \theta d \theta \int_0^{1} \int_{r^2}^{1}r dz dr=0,\]
since $\int_0^{2\pi}\cos \theta d \theta =0$.