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Given that for each a in (0,1)underset(...

Given that for each `a in (0,1)underset(x to 0)lim overset(-h)underset(h)int t^(-a)(1-t)^(a-1)dt` exits and is equal to g(a).If g(a) is differentiable in (0,1), then the value of g'((1)/(2))`, is

A

`pi//2`

B

`pi`

C

`-pi//2`

D

`0`

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The correct Answer is:
D
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