Surface Integral of a Vector Field

[aforl]

Hi guys, need some assurance here in evaluating this surface integral.

where

and


\(\displaystyle S \ : \ \ x^2 + y^2 + (z-5)^2 \ = \ 1 \) with positive orientation (outward pointing normal).


Here's what I did:
Using Green's theorem (Divergence theorem)

Anything wrong with what I did?

 

[HallsofIvy]

No, that is perfectly correct.

(Except, of course, that this has nothing to do with "differential equations" and should be in the "Calculus" section, not the "Differential Equations" section!)