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The numbers of possible continuous `f(x)` defined in `[0,1]` for which `I_1=int_0^1f(x)dx=1,I_2=int_0^1xf(x)dx=2 ,I_3=int_0^1x^2f(x)dx=4i s//a r e` 1 (b) `oo` (c) 2 (d) 0

A

`1`

B

`oo`

C

`2`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
Since `a^(2)I_(1)-2aI_(2)+I_(3)=0`
`int_(0)^(1)(a-x)^(2)f(x)dx=0`
Hence, there is no such positive function `f(x)`.
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