Answer
$$\dfrac{486}{5}$$
Work Step by Step
Let $$x= r \cos \theta ; y=r \sin \theta $$
$$I=\int_{-\pi/2}^{ \pi/2} \int_0^{3} (r^3 \cos^3 \theta+r^3 \cos \theta \sin^2 \theta) r dr d \theta\\=\int_{-\pi/2}^{ \pi/2} \cos \theta dr d \theta \times \int_0^{3} r^4 dr \\=[\sin \theta ]_{-\pi/2}^{ \pi/2}\times [\dfrac{r^5}{5}]_0^3 \\=2 \times \dfrac{243}{5} \\=\dfrac{486}{5}$$
