Compute Integral of F over S: Vector Calculus

[lembeh]

Urgent help! Vector Calculus question...

Let S be the surface given by the graph z = 4 - x² - y² above the xy-plane (that it is, where z \geq 0) with downward pointing normal, and let

F (x,y,z) = xcosz i - ycosz j + (x² + y² ) k

Compute \oint\oint_sF dS. (F has a downward pointing normal)

(Hint: Its easy to see that div F = 0 on all R³. This implies that there exists a vector field G such that F = Curl G, although it doesn't tell you what G is)

 

[lembeh]

Please help me with this. I've been working on it for 6 hours now and still can't figure it out...Your help is really appreciated!

 

[PhysicalAnomaly]

I was about to suggest something but apparently, you have to show some attempts before we can help you.