I have the following problem.
Let $(X,Y)$ be a random vector with joint density function $f(x,y)=8xy$ for $0<x<y<1$.
Find $f_X$ and $f_Y$.
My attempt was:
$f_X(x)=\int_{-\infty}^{\infty}f(x,y)dy=\int_x^1 8xydy=4x(1-x^2) $
the second equality from left to right because $x<y<1$.
But my question is, for what $x's$ is valid to say $f_X(x)=4x(1-x^2)$? because x can't be any number, it depends on "$y$" but $f_X(x)$ should depend only for x terms, right?
Thanks in advance.