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Byju's Answer
Standard XII
Mathematics
Property 4
If ∫01tan-1x-...
Question
If
1
∫
0
tan
−
1
x
cot
−
1
(
1
−
x
+
x
2
)
d
x
equals
k
,
then the value of
1
k
is
A
2.00
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B
02
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C
2
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D
2.0
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Solution
k
=
1
∫
0
tan
−
1
x
cot
−
1
(
1
−
x
+
x
2
)
d
x
…
(
1
)
⇒
k
=
1
∫
0
tan
−
1
x
cot
−
1
(
(
1
−
x
)
2
+
x
)
d
x
Applying
b
∫
a
f
(
x
)
d
x
=
b
∫
a
f
(
a
+
b
−
x
)
d
x
,
k
=
1
∫
0
tan
−
1
(
1
−
x
)
cot
−
1
(
(
1
−
1
+
x
)
2
+
(
1
−
x
)
)
d
x
⇒
k
=
1
∫
0
tan
−
1
(
1
−
x
)
cot
−
1
(
x
2
+
1
−
x
)
d
x
…
(
2
)
From
(
1
)
+
(
2
)
2
k
=
1
∫
0
tan
−
1
(
1
−
x
)
+
tan
−
1
(
x
)
cot
−
1
(
x
2
+
1
−
x
)
d
x
⇒
2
k
=
1
∫
0
tan
−
1
(
x
+
1
−
x
1
+
x
(
1
−
x
)
)
cot
−
1
(
x
2
+
1
−
x
)
d
x
⇒
2
k
=
1
∫
0
tan
−
1
(
1
x
2
+
1
−
x
)
cot
−
1
(
x
2
+
1
−
x
)
d
x
⇒
2
k
=
1
∫
0
1
d
x
⇒
k
=
1
2
∴
1
k
=
2
Suggest Corrections
0
Similar questions
Q.
If
∫
x
cos
−
1
x
√
1
−
x
2
d
x
=
−
k
[
√
1
−
x
2
cos
−
1
x
+
x
]
+
C
. what will be the value of
k
?
Q.
The value of
∫
1
0
tan
−
1
(
2
x
−
1
1
+
x
−
x
2
)
d
x
is
Q.
The value of
∫
0
1
tan
-
1
2
x
-
1
1
+
x
-
x
2
d
x
,
is
(a) 1
(b) 0
(c) −1
(d) π/4
Q.
If
1
∫
0
tan
−
1
x
cot
−
1
(
1
−
x
+
x
2
)
d
x
equals
k
,
then the value of
1
k
is
Q.
If
I
=
∫
1
0
cot
−
1
(
1
−
x
+
x
2
)
dx
=
k
∫
1
0
tan
−
1
x
dx
, then the value of k equals