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The total number for distinct x epsilon[...

The total number for distinct `x epsilon[0,1]` for which `int_(0)^(x)(t^(2))/(1+t^(4))dt=2x-1` is __________.

A

`pi`

B

`2pi`

C

`(pi)/2`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
`g(1/2)=lim_(kto 0^(+))int_(k)^(1+k)t^(-1//2)(1-t)^(-1//2)dt`
`=int_(0)^(1)(dt)/(sqrt(t-t^(2)))=int_(e)^(1)(dt)/(sqrt(1/4-(t-1/2)^(2)))=sin^(-1)((t-1/2)/(1/2))|._(0)^(1)`
`=sin^(-1)1-sin^(-1)(-1)=pi`
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