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Let f:[(1)/(2),1]to RR (the set of all r...

Let `f:[(1)/(2),1]to RR` (the set of all real numbers) be a positive, non-constant and differentiable function such that
`f'(x)lt2f(x)" and "f((1)/(2))=1`
Then the value of `int_((1)/(2))^(1)f(x)dx` lies in the interval

A

`(2e-1,2e)`

B

`(e-1,2e-1)`

C

`((e-1)/(2),e-1)`

D

`(0,(e-1)/(2))`

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