Change of Variables & the Jacobian · Medium problem

Let $R$ be the region in the first quadrant bounded by $xy=1$, $xy=3$, $y=x$, and $y=4x$. Using $u=xy$, $v=y/x$ (for which $\left|\dfrac{\partial(x,y)}{\partial(u,v)}\right|=\dfrac{1}{2v}$), find the area of $R$.