I am trying to find the volume of the region
$$\{ (x,y,z) \in (\mathbb R_0^+)^3 \mid y^2+z^2 \leq 9 \land y^2 \geq 3x \}$$
The answer is $\frac{27}{16} \pi$. The volume should be able to find using
$$V=\iint z \,\mathrm d A$$
Here you integrate the limits of $R$, where $R$ is the inferior base.
The graph for the functions would be something like this:
What I can not seem to do correctly is establish the limits for the integrals. I would appreciate any help.
I just found out the correct limits for the integrals. The solution is: $$V=\int _0^3\int _0^{\frac{y^2}{3}}\sqrt{9-y^2}dxdy\:=\frac{27\pi }{16}$$