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UPSC NDA Math Model Paper 3
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© examsnet.com
Question : 12
Total: 120
The value of the integral
π
2
∫
0
√
tan
x
1
+
√
tan
x
d
x
is
π
2
π
4
π
6
none of these
Validate
Solution:
Here, we have to find the value of the integral
π
2
∫
0
√
tan
x
1
+
√
tan
x
Let
I
=
π
2
∫
0
√
tan
x
1
+
√
tan
x
d
x
......(1)
As we know that,
b
∫
a
f
(
x
)
d
x
=
b
∫
a
f
(
a
+
b
−
x
)
d
x
I
=
π
2
∫
0
√
cot
x
1
+
√
cot
x
d
x
......(2)
Adding equation (1) and (2), we get
⇒
2
I
=
π
2
∫
0
[
√
tan
x
1
+
√
tan
x
+
√
cot
x
1
+
√
cot
x
]
d
x
⇒
2
I
=
π
2
∫
0
d
x
=
π
2
⇒
I
=
π
4
Hence, option B is the correct answer.
© examsnet.com
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