Use either Stokes' theorem or the divergence theorem to evaluate this integral in the easiest possible way.
∫∫V [itex]\cdot[/itex]ndσ over the closed surface of the tin can bounded by x2+y2=9, z = 0, z = 5, if V = 2xyi - y2j + (z + xy)k
The bolded letters are vectors.
∫∫(∇ xV) [itex]\cdot[/itex] ndσ = ∫V [itex]\cdot[/itex]dr Stokes' theorem
∫∫∫∇ [itex]\cdot[/itex]Vdτ = ∫∫V [itex]\cdot[/itex]ndσ Divergence theorem
The Attempt at a Solution
So what I did was use the divergence theorem to turn this into a volume integral. I did the ∇xV to get 2y-2y+1. But here's where I'm stuck. I can input the formula for the volume of a cylinder, right? Is that dτ? I have to integrate with respect to τ. So if 2y-2y+1 = 1, then I'm left with τ after I integrate, and is τ just ∏r2h?