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int(0)^(1) (x)/(sqrt(1 + x^(2))) dx...

`int_(0)^(1) (x)/(sqrt(1 + x^(2))) dx`

A

`- sqrt2 - 1`

B

`sqrt2 + 1`

C

`- sqrt2 + 1`

D

`sqrt2 - 1`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `I = int_(0)^(1) (x)/(sqrt(1 + x^(2)))dx`
Put `" " 1 + x^(2) = t^(2)`
`implies " " 2x dx = 2`t dt
`implies " " ` x dx = t dt
`therefore " " I = int_(1)^(sqrt2) (tdt)/(t)`
`= [t]_(1)^(sqrt2) = sqrt2 - 1`
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