Construction:

The situation looks like this –

At the intersection points, x = 2y = y²

or, y² – 2y = 0

⇒ y(y – 2) = 0

⇒ y = 0 or y = 2

So, intersection points are (0, 0) and (4, 2)

Hence, the area A enclosed is –

A =

=

= [4 – 8/3]

= 4/3 (Ans)