$f:\mathbb{R}^2\rightarrow \mathbb{R}^2, by \ f(x,y)=(x^2+y^2,x+y)$
Let $B = f^{-1}([1,4]\ \times \ [-4, \infty)\ \times \ (-2\sqrt2,2\sqrt2))$
Suppose $(X,Y)$ is a r.v. taking values in $B$ with $pdf:f(x,y)=Ce^{-\frac{x^2+y^2}{2}}I_B(x,y)$ - where C is a normalising constant.
Find $\mathbb{E}(X), \mathbb{E}^7, \mathbb{E}(|XY|(X^2+Y^2)^{-1})$
As I have not come across a normalising constant before, I am very confused as to where I should start for this question.