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UPSC NDA I 2010 Mathematics Paper
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© examsnet.com
Question : 15
Total: 120
What is
π
4
∫
−
π
4
tan
3
x
d
x
equal to?
√
3
1
3
1
2
0
Validate
Solution:
A
=
π
∕
4
∫
−
π
∕
4
tan
x
tan
2
x
d
x
=
π
∕
4
∫
−
π
∕
4
tan
x
(
sec
2
x
−
1
)
d
x
=
π
∕
4
∫
−
π
∕
4
tan
x
⋅
sec
2
x
d
x
−
π
∕
4
∫
−
π
∕
4
tan
x
d
x
Put
tan
x
=
t
or
sec
2
x
d
x
=
d
t
A
=
∫
−
1
1
t
d
t
−
π
∕
4
[
log
sec
x
]
−
π
∕
4
=
[
t
2
2
]
−
1
1
−
[
log
sec
(
π
∕
4
)
−
log
sec
(
−
π
∕
4
)
]
=
0
−
[
log
√
2
−
log
√
2
]
=
0
© examsnet.com
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