How to find the joint PDF? Ley X,Y two random variables with density
$f(x,y)=8xy \  \text{if} \  
0<x<y<1$
Find the joint distribution F(x,y).
I find that $F(x,y)=2x^2y^2-x^4\ \text{  if}  \ 0<x<y<1$ but I dont know how to find the didtribution in other points.

The five cases are:
$$F(x,y) \;=\; \begin{cases} 0 & : x<0 \vee y<0\\[1ex]\hdashline\displaystyle \int_0^y \int_0^x f(s,t)\operatorname d s\operatorname d t & : 0\leq x< y< 1 \\[1ex]\hdashline\displaystyle \int_0^y \int_0^y f(s,t)\operatorname d s\operatorname d t & : 0\leq y\leq 1, x\geq y \\[1ex]\hdashline\displaystyle \int_0^1 \int_0^x f(s,t)\operatorname d s\operatorname d t  & : 0\leq x < 1 \leq y \\[1ex]\hdashline 1 & : 1\leq x \wedge 1\leq y\end{cases}$$
