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AIEEE 2002 Math Solved Paper
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© examsnet.com
Question : 41
Total: 74
I
n
=
π
∕
4
∫
0
tan
n
x
dx
then
lim
n
→
∞
n
[
I
n
+
I
n
+
2
]
equals
1
2
1
∞
0
Validate
Solution:
I
n
+
I
n
+
2
=
π
∕
4
∫
0
tan
n
x
(
1
+
tan
2
x
)
dx
=
π
∕
4
∫
0
tan
n
x
s
e
c
2
x
dx
=
[
tan
n
+
1
x
n
+
1
]
0
π
∕
4
=
1
−
0
n
+
1
=
1
n
+
1
∴
I
n
+
I
n
+
2
=
1
n
+
1
⇒
lim
n
→
∞
n
[
I
n
+
I
n
+
2
]
=
lim
n
→
∞
n
⋅
1
n
+
1
=
lim
n
→
∞
n
n
+
1
=
lim
n
→
∞
n
n
(
1
+
1
n
)
=
1
© examsnet.com
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