The value of `int_0^(pi//2)(sqrt(cosx))/(sqrt(cos x)+sqrt(s in x))dx` is `pi//2` b. `pi//4` c. `0` d. none of these

Explanation

In this question we apply the king rule


`y=int_{0}^{frac{pi}{2}} frac{sqrt{cos x}}{sqrt{cos x}+sqrt{sin x}} d x ldots(1) `

`=int_{0}^{frac{pi}{2}} frac{sqrt{cos (frac{pi}{2}-x)}}{sqrt{cos (frac{pi}{2}-x)}+sqrt{sin (frac{pi}{2}-x)}} dx`

`=int_{0}^{frac{pi}{2}} frac{sqrt{sin x}}{sqrt{sin x}+sqrt{cos x}} d x ldots(2)`


On adding eq(1) and eq(2)


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