Joint Density function Question

Hi all,

I have been going though a Q and have no idea how to even start it:

Q:

Suppose that $\displaystyle X,Y$ have the joint distribution:

$\displaystyle f(x,y) = c(1-x^2-y^2)^{1/2}$ , $\displaystyle x^2 + y^2 \le 1$

Find c..?

Now my initial thoughts are that the bounded unit cirrcle region gives the limits of integration such that:

$\displaystyle P(X,Y \subset A)= _A\int \int f(x,y) dydx$, in our case A is bound by the unit circle, giving:

$\displaystyle = c \displaystyle \int_{-(1-x^2)^{1/2}}^{(1-x^2)^{1/2}} \int_{-(1-y^2)^{1/2}}^{(1-y^2)^{1/2}} 1-x^2-y^2 dx dy $

does this look like the right method to employ? I am not convinced..... the answer in the text book (no method though) $\displaystyle 3/2 \pi$... can anyone offer any guidance on this one??

Many thanks for reading!