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

Given that for each `a in (0,1),`
`underset(h rarr 0)(lim) int_h^(1 - h) t^-a (1 - t)^a dt`
exists. Let this limit be g(a). In addition , it is given that the function g(a) is differentiable on (0 , 1).
The value of g(1/2) is

A

`pi`

B

`2 pi`

C

`pi/2`

D

`pi/4`

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The correct Answer is:
A
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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
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  8. Suppose M = int0^(pi/2) cosx/(x+2) dx , N = int0^(pi/4) sinxcosx/(x+1)...

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  10. Let f(x) = {(int0^x abs(1 - t) dt , x gt 1),(x - 1/2 , x le 1):} Then

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  15. Let [a] denote the greatest integer which is less than or equal to a. ...

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