Showing function is not independent

Question

I need to show that this is not independent, I found that $f(x,y) = 1$ with the given restrictions on $x$ and $y$, but now to find the marginal density functions, would the integral for finding $f_x(x)$ be from $0$ to infinity and the same for $f_y(y)$ ?

Answer 1

Hints: $f_X(x)=\int_x^{\infty} f(x,y) dy$ and $f_Y(y)=\int_0^{y} f(x,y) dx$. Calculate these simple intergals. $X$ and $Y$ are independent iff $f(x,y)=f_X(x)f_Y(y)$.