$f_{XY}(x,y)=24xy1_{\{x>0,y>0,x+y\leq1\}}$
$1_{\{...\}}$ is the indicator function
I am not sure how to apply the conditions ${\{x>0,y>0,x+y\leq1\}}$ when evaluating $f_X(x)$, $f_Y(y)$ and $f_{X|Y}(x,y)$, meaning I don't know which bounds I have to use for $f_X, f_Y$ and $f_{X|Y}$
(I need it to determine $\mathbb E(X)$, $\mathbb E(Y)$ and $\mathbb E(X|Y)$)
I tried the following
$f_X(x)=\int f_{XY}(x,y)dy=\int_0^{1-x}24xydy$ for $0<x<1$ and $f_X(x)=0$ otherwise.
$f_Y(y)=\int f_{XY}(x,y)dx=\int_0^{1-x}24xydx$ for $0<y<1$ and $f_Y(y)=0$ otherwise.
$f_{X|Y}(x,y)=\frac{f_{XY}(x,y)}{f_Y(y)}=\frac{2x}{(y-1)^2}1_{\{???\}}$