Solution:

Examining the graph

we see that we have to find the points of intersection.

Now, y = 2x and y² = x+4, so y² = y/2 + 4, or 2y² - y - 8 = 0. Solving this by the quadratic formula we get

Set

The area is obtained by integrating along the y-axis. It is equal to

(65/48)*sqrt(65)