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Evaluate : int(0)^(pi//2) (cos x)/(1+sin...

Evaluate : `int_(0)^(pi//2) (cos x)/(1+sin^(2) x)dx`

Text Solution

Verified by Experts

Let sin x=t
`rArr" " cos x dx =dt`
`At x=0, " "t=sin 0=0`
`At x = pi//2, " "t=sin .(pi)/(2) =1`
`:. int_(0)^(pi//2) (cosx)/(1+sin^(2) x)dx =int_(0)^(1) (dt)/(1+t^(2))= [tan^(-1) t]_(0)^(1)`
`=tan^(-1) 1-tan^(-1) 0=(pi)/(4).`
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