The area of the region {(x, y) : y2 \(\geq\) 2x and x2 + y2 \(\leq\) 4x, x \(\geq\) 0, y \(\geq\) 0} is : 

\(\pi - \frac{8}{3}\)

The point of intersection of the curve x2 + y2 = 4x , y2 = 2x are (0, 0) and (2, 2) for x \(\geq\) 0and y \(\geq\)  0 

Area = \(\frac{}{} \pi * 4 - int_{0}^{2}\sqrt{2x}dx\)

        = \(\pi - \sqrt{2}\frac{2}{3}[x^{\frac{3}{2}}]_0^2\)

        = \(\pi - \frac{8}{3}\)