I want to evaluate ∫∫∫√(x²+y²) dV over the region in the first octant bounded by

x²+y²=2

x²+y²=√(2) x

x²+y²=z (-->paraboloid of revolution)

Here's how I've set up my cylindrical coordinates:

$\displaystyle \int\nolimits_{0}^{\tfrac{\pi }{2}} {d\theta }\int\nolimits_{\sqrt {2} \cos \theta }^{\sqrt {2} } {r^{2}dr}\int\nolimits_{0}^{r^{2}} {dz}$

Could somebody please confirm that this is the correct approach?