Question
Find the area of the region included between the parabolas y2 = 4 a x and x2 = 4 a y, a > 0.
Solution
The equations of curves are
...(1)
and 
...(2)
From (2), 
...(3)
Putting this value of y in (1),
or 
∴ x = 0, 4 a
∴ from (3), y = 0, 4 a
∴ curves (1) and (2) intersect in O (0, 0), P (4 a, 4 a).
From P. draw PM ⊥ x-axis.
Required area = Area OAPB
= Area OBPM - area OAPM
