- #1

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## Homework Statement

Use either Stokes' theorem or the divergence theorem to evaluate this integral in the easiest possible way.

∫∫

**V**[itex]\cdot[/itex]

**n**dσ over the closed surface of the tin can bounded by x

^{2}+y

^{2}=9, z = 0, z = 5, if

**V**= 2xy

**i**- y

^{2}

**j**+ (z + xy)

**k**

The bolded letters are vectors.

## Homework Equations

∫∫(

**∇**x

**V**) [itex]\cdot[/itex]

**n**dσ = ∫

**V**[itex]\cdot[/itex]d

**r**Stokes' theorem

∫∫∫

**∇**[itex]\cdot[/itex]

**V**dτ = ∫∫

**V**[itex]\cdot[/itex]

**n**dσ 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 ∏r

^{2}h?

Thanks