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UPSC NDA Math Model Paper 10
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© examsnet.com
Question : 60
Total: 120
What is the value of
2
∫
1
e
x
(
1
x
−
1
x
2
)
d
x
?
e
(
e
2
−
1
)
e
(
e
−
1
)
e
−
1
e
0
Validate
Solution:
Let, I =
2
∫
1
e
x
(
1
x
−
1
x
2
)
d
x
=
2
∫
1
(
e
x
x
)
d
x
−
2
∫
1
(
1
x
2
)
d
x
=
[
1
x
2
∫
1
e
x
d
x
]
1
2
+
2
∫
1
(
e
x
x
2
)
d
x
−
2
∫
1
(
e
x
x
2
)
d
x
=
[
1
x
(
e
x
)
]
1
2
=
1
2
(
e
2
)
−
e
=
e
(
e
2
−
1
)
Hence, option (3) is correct.
© examsnet.com
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