Calculate the rotational inertia of a uniform hollow-core cylinder of inner radius (R_{text {inner }}), outer radius

Question:

Calculate the rotational inertia of a uniform hollow-core cylinder of inner radius $R_{\text {inner }}$, outer radius $R_{\text {outer }}$, length $\ell$, and inertia $m$ about an axis parallel to the cylinder's length and passing through its center, as in Figure 11.38.

Data from Figure 11.38