To this
end, we solve the equations x2 = y and y = 4
which gives x = –2 and x = 2 Thus, the region AOBA may be stated as
the region bounded by the curve y = x 2, y = 4
and the ordinates x = –2 and x = 2 Therefore, the area of the region AOBA
= 
2
2 ydx
−∫
  [ y = (y-coordinate of Q) – (y-coordinate of P) = 4 – x 2]
= 
(
)
2
2
20
4
x
dx
−
∫
(Why )
=
2
3
0
2 4
x3
x

−




 
8
2 4 2
3


=
× −



32
3
=
Remark From the above examples, it is inferred that we can consider either vertical
strips or horizontal strips for calculating the area of the region