On a map, the western edge of a woodland is the $y$-axis and the eastern edge is the curve $x = 2\sqrt{y}$. The woodland lies between the lines $y = 1$ and $y = 9$, as in the figure. Lengths on the map are in hundreds of metres. What is the area of the woodland, in square units of the map?

Fig. 1: The blue curve x = 2 times the square root of y, rising from the origin and bending to the right. Two red dashed horizontal lines mark y = 1 and y = 9. The region between the y-axis and the curve, between these two lines, is shaded orange.