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

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

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Verified by Experts

Let `1+x^(2) =t`
`rArr " "2x dx =dt " "rArr " "x dx =(dt)/(2)`
`At x=0 , " "t=1 +0=1`
`Atx=1, " " t=1+1=2`
`"Now " int_(0)^(1) (x)/(sqrt(1+x^(2)))dx`
` =int_(1)^(2)(dt)/(2sqrt(t)) =1/2 int_(1)^(2) t^(-1//2) dt`
` =1/2 [(t^(1//2))/(1//2)]_(1)^(2) =(sqrt(2)-1).`
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