Question

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-a ,I_3=int_0^1x^2f(x)dx=a^2i s//a r e` 1 (b) `oo` (c) 2 (d) 0
A. `1`
B. `oo`
C. `2`
D. `0`

Answer 1

Correct Answer - 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)`.