Surface Integrals, Stokes & Divergence · Hard problem

A cylindrical silo's wall is $x^2+y^2=4$ (meters), $0\le z\le 5$. Uneven insulation makes heat escape through the wall at a rate per unit area of $q(x,y,z) = x^2$ W/m$^2$. Find the total heat-loss rate through the whole wall, $\displaystyle\iint_S x^2\,dS$, in watts.