`int_(0)^(1)(x)/(sqrt(1+x^(2)))dx` का मान ज्ञात कीजिए ।

Explanation

माना `1+x^(2)=t`
`rArr" "2xdx=dt`
`rArr" "xdx=(dt)/(2)`
`x = 0 " पर "t=1+0=1`
`x=1" पर "t=1+1=2`
अब `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)=(sqrt2-1)`