Chapter 14, Problem 3PS

Using a Change of variables The figure shows the region $R$ bounded by the curves

$y=\sqrt{x},y=\sqrt{2x},y=\frac{x^2}{3},\text{and}y=\frac{x^2}{4}.$

Use the change of variables $x=u^{1/3}{v}^{2/3}$ and $y=u^{2/3}{v}^{1/3}$ to find the area of the region $R$.