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JEE Main Math Class 12 Integrals Part 3 Questions
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© examsnet.com
Question : 4
Total: 100
Let
I
(
x
)
=
∫
x
2
(
x
s
e
c
2
x
+
tan
x
)
(
x
tan
x
+
1
)
2
dx
. If
I
(
0
)
=
0
, then
I
(
π
4
)
is equal to :
[6-Apr-2023 shift 1]
log
e
(
π
+
4
)
2
16
+
π
2
4
(
π
+
4
)
log
e
(
π
+
4
)
2
32
−
π
2
4
(
π
+
4
)
log
e
(
π
+
4
)
2
16
−
π
2
4
(
π
+
4
)
log
e
(
π
+
4
)
2
32
+
π
2
4
(
π
+
4
)
Validate
Solution:
I
(
x
)
=
∫
x
2
(
x
s
e
c
2
x
+
tan
x
)
(
x
tan
x
+
1
)
2
dx
Let
x
tan
x
+
1
=
t
I
=
x
2
(
−
1
x
tan
x
+
1
)
+
∫
2
x
x
tan
x
+
1
dx
I
=
x
2
(
−
1
x
tan
x
+
1
)
+
2
∫
2
x
x
tan
x
+
1
dx
I
=
x
2
(
−
1
x
tan
x
+
1
)
+
2
ln
|
x
s
i
n
x
+
cos
x
|
+
C
As I
(
0
)
=
0
⇒
C
=
0
I
(
π
4
)
=
ln
(
(
π
+
4
)
2
32
)
−
π
2
4
(
π
+
4
)
© examsnet.com
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