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JEE Main Math Class 12 Integrals Part 2 Questions
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© examsnet.com
Question : 2
Total: 100
Let the domain of the function
f
(
x
)
=
log
4
(
log
5
(
log
3
(
18
x
−
x
2
−
77
)
)
)
be
(
a
,
b
)
Then the value of the integral
b
∫
a
sin
3
x
(
sin
3
x
+
sin
3
(
a
+
b
−
x
)
)
d
x
is equal to ________.
[27 Jul 2021 Shift 1]
Your Answer:
Validate
Solution:
For domain
log
5
(
log
3
(
18
x
−
x
2
−
77
)
)
>
0
log
3
(
18
x
−
x
2
−
77
)
>
1
18
x
−
x
2
−
77
>
3
x
2
−
18
x
+
80
<
0
x
∈
(
8
,
10
)
⇒
a
=
8
and
b
=
10
I
=
b
∫
a
sin
3
x
sin
3
x
+
sin
3
(
a
+
b
−
x
)
d
x
I
=
b
∫
a
sin
3
(
a
+
b
−
x
)
sin
3
x
+
sin
3
(
a
+
b
−
x
)
2
I
=
(
b
−
a
)
⇒
I
=
b
−
a
2
(
∵
a
=
8
and
b
=
10
)
I
=
10
−
8
2
=
1
© examsnet.com
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