A point $(X,Y)$ in the Cartesian plane is uniformly distributed within the unit circle if $X$ and $Y$ have joint density:
$$f(x,y) = \begin{cases} \frac{1}{π} & \mathrm{x^2+y^2} \le 1 \\ 0 & \mathrm{otherwise} \end{cases} $$
Find the marginal densities $f_X$ and $f_Y$ and state whether $X$ and $Y$ are independent or not. Provide a mathematical justification for your answer.
I am really confused, I don't know how to set up the two integrals, please help :)
