Limitations of the divergence theorem

[blade123]

Homework Statement

Evaluate the surface integral F * dr, where F=<0, y, -z> and the S is y=x^2+y^2 where y is between 0 and 1.

Homework Equations

Divergence theorem

The Attempt at a Solution

I just got out of my calculus final, and that was a problem on it. I used the divergence theorem and got div F = 0 + 1 - 1 =0

Therefore the triple integral and therefore the surface integral will return 0. Is this true? I thought it was too easy, I can't see why it wouldn't be true.

Is there a limitation I glossed over?

 

[Whovian]

Don't think so, that should work. Try evaluating the surface integral and seeing if it also returns 0.