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Let `f:[1/2,1]->R` (the set of all real numbers) be a positive, non-constant, and differentiable function such that `f^(prime)(x)<2f(x))a n df(1/2)=1` . Then the value of `int_(1/2)^1f(x)dx` lies in the interval (a) `(2e-1,2e)` (b) `(3-1,2e-1)` `((e-1)/2,e-1)` (d) `(0,(e-1)/2)`

A

`( 2e - 1,2e)`

B

`(e-1,2-1)`

C

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

D

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

Text Solution

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The correct Answer is:
D
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