Converting to Cylindrical Coordinates for Triple Integration

[TheAntithesis]

I don't want the answer, just a little help getting there.
The question asks to integrate this: Triple integral

I'm thinking to convert it to cylindrical but I have no idea how to convert the bounds. I can convert the actual expression z/sqrt(x^2+y^2) into cylindrical no problem. If I had some picture as to what the bounds look like then I might be able to get somewhere. Any help would be greatly appreciated.

 

[vela]

Forget about z for now. Sketch the region bounded by the limits of the integrals in the xy-plane.

 

[SammyS]

In Latex:

\int_0^2 \int_0^{\sqrt{4-x^2}} \int_0^{(x^2+y^2)/2} \frac{z}{\sqrt{x^2+y^2}}\ dz\, dy\, dx