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Byju's Answer
Standard XII
Mathematics
Scalar Matrix
If f x = begi...
Question
If
f
(
x
)
=
∣
∣ ∣
∣
1
2
x
3
x
2
3
a
27
1
3
9
∣
∣ ∣
∣
and
∫
3
0
f
(
x
)
d
x
=
0
, then a is equal to
A
3
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B
6
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C
9
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D
any real number
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Solution
The correct option is
D
any real number
∫
3
0
f
(
x
)
d
x
=
∣
∣ ∣ ∣
∣
∫
3
0
d
x
∫
3
0
2
x
d
x
∫
3
0
3
x
2
d
x
3
a
27
1
3
9
∣
∣ ∣ ∣
∣
=
∣
∣ ∣
∣
3
9
27
3
a
27
1
3
9
∣
∣ ∣
∣
∫
3
0
f
(
x
)
d
x
=
0
∴
a
∈
any real number.
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Similar questions
Q.
If (2
3
)
2
= 4
x
, then 3
x
=
(a) 3
(b) 6
(c) 9
(d) 27