The point of intersection of the
Parabolas y² = 4x and x² = 4y are (0, 0) and (4, 4)

Now, the area of the region OAQBO bounded by curves y2 = 4x and x2 = 4y

4

∫

0

(2√x.

x2

4

) dx = [2

x 3 2

3 2

−

x3

12

]04 =

32

3

−

16

3

=

16

3

sq units ………..(i)
Again, the area of the region OPQAO bounded by the curves x2 = 4y, x = 0, x = 4 and the x-axis,

4

∫

0

x2

4

dx = [

x3

12

]04 = (

64

12

) =

16

3

sq units ……….(ii)
Similarly, the area of the region OBQRO bounded by the curve y2 = 4x, the y-axis, y = 0 and y = 4

4

∫

0

y2

4

dy = [

y3

12

]04 =

16

3

sq units ... (iii)
From (i), (ii), and (iii) it is concluded that the area of the region OAQBO = area of the region OPQAO = area of the region OBQRO, i.e., area bounded by parabolas
y2 = 4x and x2 = 4y divides the area of the square into three equal parts.