n
n
n
n
n
e
e
e
e
n
→∞


+
+
+
+






Using the sum to n terms of a G P , where a = 1, 
n2
r
=e
, we have
2
0
∫xe dx
=
2
2
1
–1
2 lim
[
]
1
n
n
n
n
ne
e
→∞
−
 = 
2
2
1
–1
2 lim
–1
n
n
n ee
→∞








=
2
2
2 (
–1)
–1
lim
2
2
n
n
e
e
n
→∞




⋅






 = e2 – 1
[using 
0
(
1)
lim
1
h
h
e
h
→
−
= ]
EXERCISE 7 8
Evaluate the following definite integrals as limit of sums