Let R be the region inside both loops of the function $r = 2+4\cos(θ)$. Then I was first asked to find the value of $C_1$ so that $f(r,θ)$ is a joint density function. So, $f(r,θ) = C_1(1-r^2)$ , if $(r,θ)∈R$ but the issue is I am not exactly sure how to do this in my mind I am thinking I could integrate over the function $1-r^2$ first and then $2+4\cos(θ)$ to find the ratio but no text book does this.
So how exactly should I go about this because all the examples in my text book provides bounds which makes it easy but this one does not. I know I can find the bounds easy but I am not sure what I am looking for should I just use the bounds of the function $z = 1-r^2$ for all parts thats inside the function $r=2+4\cos(θ)$?
Here is a screen shot of the problem.