13
Fig 8 14
dA = [f (x) – g(x)] dx, and the total area A can be taken as
A = 
[ ( )
( )]
b
a f x
−g x dx
∫
Alternatively,
A = [area bounded by y = f (x), x-axis and the lines x = a, x = b]
– [area bounded by y = g (x), x-axis and the lines x = a, x = b]
=
( )
( )
b
b
a
a
f x dx
g x dx
−
∫
∫
 =
[
]
( )
( )
,
b
a f x
g x
dx
−
∫
where f (x) ≥ g (x) in [a, b]
If f (x) ≥ g (x) in [a, c] and f (x) ≤ g (x) in [c, b], where a < c < b as shown in the
Fig 8 14, then the area of the regions bounded by curves can be written as
Total Area = Area of the region ACBDA + Area of the region BPRQB
 =
[
]
[
]
( )
( )
( )
( )
c
b
a
c
f x
g x
dx
g x
f x dx
−
+
−
∫
∫
368
MATHEMATICS
Y
O
P�(4,�4)
C�(4,�0)
Y�
X�
X
Q�(8,�0)
Fig 8 16
Example 6 Find the area of the region bounded by the two parabolas y = x2 and y2 = x