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int (dx)/sqrt(2x-x^2)...

`int (dx)/sqrt(2x-x^2)`

A

`sin^(-1)(x+1)+C`

B

`sin^(-1)(x-2)+C`

C

`sin^(-1)(x-1)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`sqrt(2x-x^(2))=sqrt(1-(1-2x+x^(2)))=sqrt(1-(x-1)^(2))`
`therefore I=int (dx)/(sqrt(1-(x-1)^(2)))=int (dt)/(sqrt(1-t^(2))),"where"(x-1)=t`
`sin^(-1)t+c =sin ^(-1)(x-1)+C.`
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