Given the joint probability density function of $X$ and $Y$ is $$ f(x,y)=\cases{xy \exp\bigl(-\textstyle{1\over2}(x^2+y^2)\bigr),&$x>0,y>0$\cr 0\phantom{\Bigl[},& elsewhere.} $$ Find $P(X^2+Y^2>4)$.
What approach should I use to solve this question? Transformation?
Hope someone can help me !_!