Flux Integral for a Surface Above a Disc with Downward Orientation

[Instinctlol]

QUESTION: Compute the flux of the vector field, F , through the surface, S.

F = xi+yj+zk

S is the part of the surface z = x^2 + y^2 above the disc x^2 + y^2 ≤ 4 , oriented downward.

I am just wondering why the integrand is from o to 4 while the radius is only 2.

 

[HallsofIvy]

It isn't. That's incorrect. It should be 2.

 

[Instinctlol]

My solution guide says otherwise, along with my online homework

 

[Instinctlol]

It isn't. That's incorrect. It should be 2.

I just emailed my teacher and he said there was an error in the online homework. The correct answer is indeed used with radius 2. Sorry about that.