Q45 of 261 Page 811

Evaluate the following integrals


Let

Let sin x- cos x=t


⇒ (cos x + sin x)dx=dt.


When x=0, t=-1 and , t=1.


Also, t2=(sin x – cos x)2


=sin2x+cos2x-2sinxcosx


=1-2sinxcosx


or



Hence


Let t=sin y


⇒ dt=cos y dy.


Also, when t=-1,


and when t=1, .




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