Evaluate $\iint_{0Let $$f(x,y)=\begin{cases}xy &\text{ if } 0<x<y<1, \\ 0 &\text { otherwise. }\end{cases}$$  Evaluate the  integral $\displaystyle \iint f(x,y)\,dx\,dy$.
I'm having trouble with the limits on integration. 

$$\int\int f(x,y)\,dx\,dy = \int_{y=0}^1\int_{x=0}^y xy\ dx\ dy=\int_{y=0}^1 \frac{y^3}{2}\ dy = \frac{1}{8}$$
