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Byju's Answer
Standard XII
Physics
Definite Integrals
STATEMENT-1 :...
Question
STATEMENT-1 : The value of
π
/
6
∫
π
/
3
1
1
+
tan
3
x
d
x
is
π
12
and
STATEMENT-2 :
b
∫
a
f
(
x
)
d
x
=
b
∫
a
f
(
a
+
b
+
x
)
d
x
A
Both statement I and statement II are correct and statement II is the correct explanation of statement I
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B
Both statement I and statement II are correct but statement II is not the correct explanation of statement I
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C
Statement II is correct but statement I is incorrect
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D
Statement I is correct but statement II is incorrect
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Solution
The correct option is
D
Statement I is correct but statement II is incorrect
We know that
b
∫
a
f
(
x
)
d
x
=
b
∫
a
f
(
a
+
b
−
x
)
d
x
⇒
Statement-2 is false
Suggest Corrections
0
Similar questions
Q.
Statement - I : The value of the integral
∫
π
/
3
π
/
6
d
x
1
+
√
tan
x
is equal to
π
6
Statement -II :
∫
b
a
f
(
x
)
d
x
=
∫
b
a
f
(
a
+
b
−
x
)
d
x
Q.
Assertion :If
n
>
1
then Statement -1:
∫
∞
0
d
x
1
+
x
n
=
∫
1
0
d
x
(
1
−
x
n
)
1
/
n
Reason: Statement -2:
∫
b
a
f
(
x
)
d
x
=
∫
b
a
f
(
a
+
b
−
x
)
d
x
Q.
∫
b
a
f
(
a
+
b
−
x
)
d
x
=
∫
b
a
f
(
x
)
d
x
is true
Q.
Assertion :If
n
>
1
then
∫
∞
0
d
x
1
+
x
n
=
∫
1
0
d
x
(
1
−
x
n
)
1
/
n
Reason:
∫
b
a
f
(
x
)
d
x
=
∫
b
a
f
(
a
+
b
−
x
)
d
x
Q.
The set of real values of
t
∈
[
−
π
2
,
π
2
]
satisfying
2
sin
t
=
1
−
2
x
+
5
x
2
3
x
2
−
2
x
−
1
,
∀
x
∈
R
−
{
−
1
3
,
1
}
lies in the interval
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