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NIMCET 2013 Question Paper with solutions
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© examsnet.com
Question : 6
Total: 120
If
I
n
=
π
4
∫
0
t
a
n
n
θ dθ , then
I
8
+
I
6
equals :
1/4
1/5
1/6
1/7
Validate
Solution:
Given
I
n
=
π
4
∫
tan
n
θ
d
θ
⇒
I
n
=
π
4
∫
0
tan
n
−
2
θ
tan
2
θ
d
θ
⇒
I
n
=
π
4
∫
0
tan
n
−
2
θ
(
sec
2
θ
−
1
)
d
θ
[∵
tan
2
θ
=
(
sec
2
θ
−
1
)
]
⇒
I
n
=
π
4
∫
0
tan
n
−
2
θ
sec
2
θ
−
π
4
∫
0
tan
n
−
2
θ
d
θ
⇒
I
n
+
I
n
−
2
=
1
∫
0
t
n
−
2
d
t
=
[
t
n
−
1
n
−
1
]
0
1
[∵ let
tan
θ
=
t
]
⇒
I
n
+
I
n
−
2
=
1
n
−
1
Now, putting n = 8,we get
I
8
+
I
8
−
2
=
1
8
−
1
⇒
I
8
+
I
6
=
1
7
© examsnet.com
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