By using the properties of definite integrals, evaluate the integrals`int0pi/2(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx`

Explanation

To evaluate the integral \( I = \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \) using the properties of definite integrals, we can follow these steps:

### Step 1: Define the Integral
Let
\[ I = \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \]

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