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Byju's Answer
Standard XII
Mathematics
Property 3
∫1 / 81 / 2[l...
Question
If
1
/
2
∫
1
/
8
[
ln
[
1
x
]
]
d
x
is equal to
a
b
,
where
a
and
b
are coprime, then the value of
b
−
4
a
is
(
[
.
]
denotes the greatest integer function)
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Solution
I
=
1
/
2
∫
1
/
8
[
ln
[
1
x
]
]
d
x
=
1
/
7
∫
1
/
8
[
ln
7
]
d
x
+
1
/
6
∫
1
/
7
[
ln
6
]
d
x
+
1
/
5
∫
1
/
6
[
ln
5
]
d
x
+
1
/
4
∫
1
/
5
[
ln
4
]
d
x
+
1
/
3
∫
1
/
4
[
ln
3
]
d
x
+
1
/
2
∫
1
/
3
[
ln
2
]
d
x
Since
[
ln
2
]
=
0
and
[
ln
3
]
=
[
ln
4
]
=
[
ln
5
]
=
[
ln
6
]
=
[
ln
7
]
=
1
∴
I
=
1
/
3
∫
1
/
8
1
d
x
=
5
24
⇒
a
=
5
,
b
=
24
∴
b
−
4
a
=
4
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