Area bounded by parabola y2 = x and straight line 2y = x is
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)