� Second fundamental theorem of integral calculus
Let f be a continuous function of x defined on the closed interval [a, b] and
let F be another function such that 
F( )
( )
d
x
f x
dx
=
 for all x in the domain of
f, then 
[
]
( )
F( )
C
F ( )
F ( )
b
b
a
a f x dx
x
b
a
=
+
=
−
∫ This is called the definite integral of f over the range [a, b], where a and b
are called the limits of integration, a being the lower limit and b the
upper limit —�
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APPLICATION OF INTEGRALS         359
Fig 8 1
� One should study Mathematics because it is only through Mathematics that
nature can be conceived in harmonious form