(
( – 1) ]
h
h f a
f a
h
f a
n
h
→
+
+
+
+
+
or
( )
b
∫a f x dx
 =
( – ) lim1
[ ( )
(
) (
( –1) ]
n
b
a
f a
f a
h
f a
n
h
→∞n
+
+
+
+
+ (6)
where
h =
–
0
b
a
as n
n
→
→ ∞
The above expression (6) is known as the definition of definite integral as the limit
of sum Remark The value of the definite integral of a function over any particular interval
depends on the function and the interval, but not on the variable of integration that we
INTEGRALS         333
choose to represent the independent variable