Q39 of 261 Page 811

Evaluate the following integrals


Let

Let √x=t


⇒


or


dx=2tdt.


When, x=0, t=0


and when x=1, t=1.


Hence,



Using integration by parts, we get




Let t=sin y


⇒ dt=cos y dy.


When t=0, y=0, when t=1, .


….. (1)


Using, , we get


…..(2)


Adding (1) and (2), we get




Hence,



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