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Byju's Answer
Standard XII
Mathematics
Properties of Composite Function
Let J =∫01 x ...
Question
Let
J
=
1
∫
0
x
1
+
x
8
d
x
.
Consider the following assertions:
I.
J
>
1
4
II.
J
<
π
8
Then
A
Only I is true
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B
Only II is true
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C
Both I and II are true
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D
neither I nor II is true
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Solution
The correct option is
A
Only I is true
For
0
<
x
<
1
x
4
>
x
8
⇒
1
+
x
4
>
1
+
x
8
⇒
1
1
+
x
4
<
1
1
+
x
8
⇒
x
1
+
x
4
<
x
1
+
x
8
⇒
1
∫
0
x
1
+
x
4
d
x
<
1
∫
0
x
1
+
x
8
d
x
⇒
J
>
1
∫
0
x
1
+
x
4
d
x
⇒
J
>
π
8
>
1
4
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1
Similar questions
Q.
Let
I
=
∫
1
0
√
1
+
√
x
1
−
√
x
d
x
a
n
d
J
=
∫
1
0
√
1
−
√
x
1
+
√
x
d
x
.
Then which of the following statement(s) is/are correct?
Q.
Let
J
=
∫
1
2
0
(
1
4
−
x
2
)
4
d
x
a
n
d
K
=
∫
1
2
0
x
4
(
1
−
x
)
4
d
x
,
then
Q.
Let
j
=
√
−
1
. Then one value of
j
j
is
Q.
Let
I
=
∫
π
0
c
o
s
x
(
x
+
2
)
2
d
x
and
J
=
∫
π
2
0
s
i
n
2
x
x
+
1
d
x
, then the value of 'J' terms of 'I' equals
Q.
If
J
=
1
∫
0
x
1
+
x
8
d
x
Consider the following statements
I
)
J
>
1
4
I
I
)
J
>
π
4
Then
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