`int_0^(pi//2)(sinx)/(sin x+cos x)dx` equals to `pi//2` b. `pi//4` c. `pi//3` d. `pi`

Explanation

`pi / 4`

We have,


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

`Rightarrow I=int_{0}^{frac{pi}{2}} frac{sin (frac{pi}{2}-x)}{sin (frac{pi}{2}-x)+cos (frac{pi}{2}-x)} d x `

`Rightarrow I=int_{0}^{frac{pi}{2}} frac{cos x}{cos x+sin x} d x `

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


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