Let $\vec{F}(x,y,z) = 2 y \vec{j}$ and $S$ be the closed vertical cylinder of height $5$, with its base a circle of radius $2$ on the xy-plane centered at the origin. $S$ is oriented outward. (a) Compute the flux of $\vec{F}$ through $S$ using the divergence theorem. Flux = $\displaystyle \iint\limits_S \vec{F} \cdot d\vec{A}$ = (b) Compute the flux directly. Flux out of the top = Flux out of the bottom = Flux out of the vertical sides =

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