## Thomas' Calculus 13th Edition

$\frac{\pi h a^4}{10}$
$I_2= \int^{2\pi}_0 \int^a_0 \int^h _{\frac{h}{a}r}(x^2+y^2)$ dz r dr d $\theta$ =$\int ^{2\pi}_0 \int^a_0 \int^h _{\frac{hr}{a}}r^3$ dz dr d $\theta$ =$\int^{2\pi}_0 \int^{a}_0 (hr^3-\frac{hr^4}{a})$ dr d $\theta$ =$\int^{2\pi}_0 h[\frac{r^4}{4}-\frac{r^5}{5a}]^a_0 d\theta$ =$\int^{2\pi}_0 h(\frac{a^4}{4}-\frac{a^5}{5a})d\theta$ =$\frac{ha^4}{20} \int^{2\pi}_0 d\theta$ =$\frac{\pi h a^4}{10}$