Verifying divergence theorem with an example

[grissom]

Verify the divergence theorem when F=xi+yj+zk and sigma is the closed surface bounded by the cylindrical surface x^2+y^2=1 and the planes z=0, z=1.

I've done the triple integral side of the equation and got 3pi but don't know how to solve the flux side of the equation \oint\ointF.ds.

Any help is appreciated. Also, this is my first time using this, so the symbols may be a bit off.

 

[Fightfish]

You have to break up the cylindrical surface into three parts: the top, bottom and the "sides" for the lack of a better word. Then, perform the integral of F over each surface and finally, sum them up.