Probability of area of a rectangle (uniform distribution) Given $X\sim U(0,2)$ and $Y\sim U(0,3)$ which are length and width of a rectangle (respectively). I want to find the probability of the area of the rectangle less than 1.
The hint is the joint density $f(x,y) = 1/6$ for $0\leq x \leq 2$ and $0 \leq y \leq 3$. 
So, f(x,y) = 0, otherwise.
The answer is 0.4653, but never explained why.

Hint:
Try  to understand whether the following is true and evaluate it. 
\begin{align}
Pr(XY < 1) = \int_0^2 \int_0^{\min(3,\frac1x)}f(x,y)dydx
\end{align}
