Wikipedia's article on moment of inertia provides examples of how to derive the moments of inertia for different bodies:

$$I_P=\iiint_Q p(x,y,z)||\mathbf{r}||^2 dV$$

It gives an example of how to derive the moment of inertia for a thin rod:

$$I_{C,rod}=\iiint_Q p(x,y,z)||\mathbf{r}||^2dV=\int_{-\frac{l}{2}}^{\frac{l}{2}} px^2s dx=\left.px\frac{x^3}{3}\right\rvert_{-\frac{l}{2}}^\frac{l}{2}=\frac{ps}{3}\left(\frac{l^3}{8}+\frac{l^3}{8}\right)=\frac{ml^2}{12}$$

That was pretty straightfoward, but I don't understand why you need a double integral for the example that follows, the derivation for a thin disk:

$$I_{C,disk}=\iiint_Q p(x,y,z)||\mathbf{r}||^2dV=\int_0^{2\pi}\int_0^Rpr^2sr *dr*d\theta=2{\pi}ps\frac{R^4}{4}=\frac{1}{2}mR^2$$

I know it is because $V({r,\theta})$ is a function of two variables, but I still don't understand where those limits come from. Could someone please explain?

Wikipedia's article on moment of inertia provides examples of how to derive the moments of inertia for different bodies:

$$I_P=\iiint_Q p(x,y,z)||\mathbf{r}||^2 dV$$

It gives an example of how to derive the moment of inertia for a thin rod:

$$I_{C,rod}=\iiint_Q p(x,y,z)||\mathbf{r}||^2dV=\int_{-\frac{l}{2}}^{\frac{l}{2}} px^2s dx=\left.px\frac{x^3}{3}\right\rvert_{-\frac{l}{2}}^\frac{l}{2}=\frac{ps}{3}\left(\frac{l^3}{8}+\frac{l^3}{8}\right)=\frac{ml^2}{12}$$

That was pretty straightfoward, but I don't understand why you need a double integral for the example that follows, the derivation for a thin disk:

$$I_{C,disk}=\iiint_Q p(x,y,z)||\mathbf{r}||^2dV=\int_0^{2\pi}\int_0^Rpr^2sr\, dr\, d\theta=2{\pi}ps\frac{R^4}{4}=\frac{1}{2}mR^2$$

I know it is because $V({r,\theta})$ is a function of two variables, but I still don't understand where those limits come from. Could someone please explain?