Answer
$I = \frac{1}{3}ML^2$
Work Step by Step
Equation (9.20) states: $I = \int~r^2~dm$.
Let $\rho$ be the length density of the disk.
$I = \int_{0}^{L}~r^2~\rho~(dr)$
$I = \rho\int_{0}^{L}~r^2~dr$
$I = \rho~(\frac{r^3}{3})\vert_{0}^{L}$
$I = \rho~(\frac{L^3}{3})$
$I = \frac{1}{3}~\rho~(L)~L^2$
$I = \frac{1}{3}ML^2$
