Given the cylindrical shell shown, show that

$I_{}=\frac{1}{2}m{r}^2+\frac{1}{12}m{l}^2$

$I_{x_1{x}_1}=\frac{1}{2}m{r}^2+\frac{1}{3}m{l}^2$

$I_z=m{r}^2$