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JEE Main Math Class 12 Integrals Part 3 Questions
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© examsnet.com
Question : 18
Total: 100
If
3
∫
1
3
|
log
e
x
|
dx
=
m
n
log
e
(
n
2
e
)
, where
m
and
n
are coprime natural numbers, then
m
2
+
n
2
−
5
is equal to ________.
[25-Jan-2023 Shift 2]
Your Answer:
Validate
Solution:
3
∫
1
3
|
ℓ
nx
|
dx
=
1
∫
1
3
(
−
ℓ
nx
)
dx
+
3
∫
1
(
ℓ
nx
)
dx
=
−
[
x
ℓ
nx
−
x
]
1
∕
3
1
+
[
x
ℓ
nx
−
x
]
1
3
=
−
[
−
1
−
(
1
3
ℓ
n
1
3
−
1
3
)
]
+
[
3
ℓ
n
3
−
3
−
(
−
1
)
]
=
[
−
2
3
−
1
3
ℓ
n
1
3
]
+
[
3
ℓ
ln
3
−
2
]
=
−
4
3
+
8
3
ℓ
nn
3
=
4
3
(
2
ℓ
n
3
−
1
)
=
4
3
(
ℓ
n
9
e
)
∴
m
=
4
,
n
=
3
Now,
m
2
+
n
2
−
5
=
16
+
9
−
5
=
20
© examsnet.com
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