Let S be the surface of the cylinder bounded by x2+y2=4 and the planes z=0 and z=3, with closed top and open bottom. Let F(x, y,z)=(x3+3xy2)i+(xz+arctanz)j+xz2k. Find ∬SF⋅dS, where S is oriented outward. [Hint: S is not a closed surface. Also consider the integral of F over the missing bottom of S (with downward orientation) and apply the Divergence Theorem.]

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