I need to write the following integral as a single integral. Not sure how to do it. I did manage to make it a double integral by having $x^2+y^2=r^2$.
The domain is: $V=\{(x,y,z)|x^2+y^2\leq 1, 0\leq z\leq 2\sqrt{x^2+y^2}, x\geq 0\}$
The integral to be calculated on this domain: $$\iiint f(z)dxdydz=\int f(z)\square dz$$
I need to find $\square$.
You're right, the first step is to write it in cylindrical coordinates: $$ \iiint f(z) dxdydz = \int_0^{2\pi} \int_0^1 \int_0^{2r} r f(z) dzdrd\theta = 2\pi \int_0^1 \int_0^{2r} r f(z) dz dr, $$ and now change the order of integration so you integrate $dz$ first.