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`int_0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx)) dx`

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`"Let " I= int_(0)^(pi//2) (sqrt(sin x))/(sqrt(sinx +)sqrt(cos x))dx......(1)`
`" then "I= int_(0)^(pi//2) (sqrt(sin((pi)/(2)-x)))/(sqrt(sin((pi)/(2)-x))+sqrt(cos((pi)/(2)-x)))dx`
`[ :' int_(0)^(a) f(x) dx= int_(0)^(a) f(a-x)dx]`
`rArr I = int_(0)^(pi//2) (sqrt(cosx))/(sqrt(cos x)+sqrt(sinx))dx " "....(2)`
Adding equations (1) and (2)
`2I =int_(0)^(pi//2) (sqrt(sin x)+sqrt(cos x))/(sqrtsinx+sqrt(sinx))dx`
`=int_(0)^(pi//2) 1dx =[x]_(0)^(pi//2)=(pi)/(2)`
`rArr I=(pi)/(4)`
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