Product of two uniforms exceeding one half

$X$ and $Y$ are independent and uniform on $(0,1)$. Find $\mathbb{P}[XY>\tfrac12]$, rounded to two decimal places.

About $0.15$. The region $xy>\tfrac12$ in the unit square needs $x>\tfrac12$ and $y>\tfrac{1}{2x}$, so the area is $\int_{1/2}^1\left(1-\tfrac{1}{2x}\right)dx=\tfrac12(1-\ln2)\approx0.153$.