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JEE Main Math Class 12 Integrals Part 4 Questions
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© examsnet.com
Question : 2
Total: 51
If
π
4
∫
0
s
i
n
2
x
1
+
s
i
n
x
cos
x
dx
=
1
a
log
e
(
a
3
)
+
π
b
√
3
, where a,
b
∈
N
, then
a
+
b
is equal to ________
[4 Apr 2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
π
2
∫
0
s
i
n
2
x
1
+
1
2
s
i
n
2
x
dx
=
π
4
∫
0
1
−
cos
2
x
2
+
s
i
n
2
x
dx
∫
1
2
+
s
i
n
2
x
−
∫
cos
2
x
2
+
s
i
n
2
x
(I) - (I
2
)
(
I
1
)
=
∫
dx
2
+
2
tan
x
1
+
tan
2
x
π
4
∫
0
s
e
c
2
xdx
2
tan
2
x
+
2
tan
x
+
2
tan
x
=
t
1
2
1
∫
0
dt
(
t
+
1
2
)
2
+
3
4
=
π
6
√
3
I
2
=
π
∕
4
∫
0
cos
2
x
2
+
s
i
n
2
x
dx
=
1
2
(
ln
3
2
)
I
1
−
I
2
=
1
√
3
π
6
+
1
2
ln
2
3
⇒
a
=
2
,
b
=
6
Ans. 8
© examsnet.com
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