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JEE Main Math Class 12 Integrals Part 3 Questions
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© examsnet.com
Question : 34
Total: 100
If
π
∫
0
5
cos
x
(
1
+
cos
x
cos
3
x
+
cos
2
x
+
cos
3
x
cos
3
x
)
dx
1
+
5
cos
x
=
k
π
16
, then
k
is equal to ______.
[1-Feb-2023 Shift 2]
Your Answer:
Validate
Solution:
I
=
π
∫
0
5
cos
x
(
1
+
cos
x
cos
3
x
+
cos
2
x
+
cos
3
x
cos
3
x
)
1
+
5
cos
x
dx
I
=
π
∫
0
5
−
cos
x
(
1
+
cos
x
cos
3
x
+
cos
2
x
+
cos
3
x
cos
3
x
)
1
+
5
cos
x
dx
2
I
=
π
∫
0
(
1
+
cos
x
cos
3
x
+
cos
2
x
+
cos
3
x
cos
3
x
)
dx
not
I
=
not
2
π
2
∫
0
(
1
+
cos
x
cos
3
x
+
cos
2
x
+
cos
3
x
cos
3
x
)
dx
I
=
π
2
∫
0
(
1
+
s
i
n
x
(
−
s
i
n
3
x
)
+
s
i
n
2
x
−
s
i
n
3
x
s
i
n
3
x
)
dx
2
I
=
π
2
∫
0
(
3
+
cos
4
x
+
cos
3
x
cos
3
x
−
s
i
n
3
x
s
i
n
3
x
)
dx
2
I
=
π
2
∫
0
3
+
cos
4
x
+
(
cos
3
x
+
3
cos
x
4
)
cos
3
x
−
s
i
n
3
x
(
3
s
i
n
x
−
s
i
n
3
x
4
)
dx
2
I
=
π
2
∫
0
(
3
+
cos
4
x
+
1
4
+
3
4
cos
4
x
)
dx
2
I
=
13
4
×
π
2
+
7
4
(
s
i
n
4
x
4
)
0
π
2
⇒
I
=
13
π
16
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