The value of difinite integral int(0)^(1...

The value of difinite integral `int_(0)^(1)=(dx)/(sqrt((x+1)^(3)(3x+1)))` equals

A

`sqrt2-1`

B

`tan.(pi)/(12)`

C

`tan.(5pi)/(12)`

D

none of these

Verified by Experts

The correct Answer is:

A

`I=int_(0)^(1)(dx)/((x+1)sqrt((x+1)(3(x+1)-2)))`
Put `x+1=(1)/(t)`
`therefore" "I=int_(1)^(1//2)(dt)/(sqrt(3-2t))=sqrt2-1`

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