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JEE Main Math Class 12 Integrals Part 2 Questions
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© examsnet.com
Question : 5
Total: 100
The value of the definite integral
5
π
∕
24
∫
π
∕
24
d
x
1
+
3
√
tan
2
x
is
[25 Jul 2021 Shift 1]
π
3
π
6
π
12
π
18
Validate
Solution:
Let
I
=
5
π
∕
24
∫
π
∕
24
(
cos
2
x
)
1
∕
3
(
cos
2
x
)
1
∕
3
+
(
sin
2
x
)
1
∕
3
d
x
.......(i)
⇒
I
=
5
π
∕
24
∫
π
∕
24
(
cos
{
2
(
π
4
−
x
)
}
)
1
3
(
cos
{
2
(
π
4
−
x
)
}
)
1
3
+
(
sin
{
2
(
π
4
−
x
)
}
)
1
3
d
x
{
b
∫
a
f
(
x
)
d
x
=
b
∫
a
f
(
a
+
b
−
x
)
d
x
}
So
I
=
5
π
∕
24
∫
π
∕
24
(
sin
2
x
)
1
∕
3
(
sin
2
x
)
1
∕
3
+
(
cos
2
x
)
1
∕
3
d
x
.
.......(ii)
Hence
2
I
=
5
π
∕
24
∫
π
∕
24
d
x
[
(
i
)
+
(
i
i
)
]
⇒
2
I
=
4
π
24
⇒
I
=
π
12
© examsnet.com
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