APPLICATION OF INTEGRALS         377
� The area of the region enclosed between two curves y = f (x), y = g (x) and
the lines x = a, x = b is given by the formula,
[
]
Area
( )
( )
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], a < c < b, then
[
]
[
]
Area
( )
( )
( )
( )
c
b
a
c
f x
g x dx
g x
f x dx
=
−
+
−
∫
∫ Historical Note
The origin of the Integral Calculus goes back to the early period of development
of Mathematics and it is related to the method of exhaustion developed by the
mathematicians of ancient Greece This method arose in the solution of problems
on calculating areas of plane figures, surface areas and volumes of solid bodies
etc In this sense, the method of exhaustion can be regarded as an early method
of integration