Find the area of the region {(x, y): x2 ≤ y ≤ |x|}.
Or
Find the area of the region bounded by the parabola y = x2 and y = |x|.
The given region is
This region is the intersection of the following regions
Consider the equations
...(1)
y = x ...(2)
and y = -x ...(3)
From (1) and (2), we get
from (2), y = 0, 1
∴ curve (1) and (2) intersect in the points O (0, 0) and A (1, 1).
Similarly, curves (1) and (3) intersect in the points O (0, 0) and B (-1, 1)
Required area = area of shaded region = 2 (area of region OAO)
