ज्ञात करें `y = int (dX)/(""_((1+x^2)^(3/2)))` तब जब x=0, y=0`.

Explanation

माना की `x = tan theta,` तो `dx = sec^2 theta d theta`
अब, `y = int (dx)/(""_((1+x^2)^(3/2)))=int (sec^3 theta)/(""_((1+tan^(2)theta)^(3/2)))d theta = int (sec^(2) theta)/(""(sec^2 theta)^(3/2))d theta`
`=int (sec^2 theta)/(sec^3 theta) d theta= int (d theta)/(sec theta)=int cos theta d theta = sin theta +c`
अतः `y = sin theta + c =x/(sqrt(1+x^2))+c" ...(1)"`
`[ tan theta= x = x/1 " ":." "sin theta= x/sqrt(1^2 +x^2)]`
प्रशन से जब, `x = 0, y = 0" ":." "` (1) से, ` 0=0+c" ":.c = 0`
अतः (1) से, `y = x/(sqrt(x+x^2))" ":.` जब `x=1, y =1/sqrt2`