Question

Value of \[ \int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sin x + \cos x} \, dx \]

• A. \( \frac{\pi}{2} \)
• B. \( \frac{\pi}{4} \)
• C. \( \frac{\pi}{6} \)
• D. None of these

Hint:

To evaluate integrals involving trigonometric functions, use symmetry and known standard integrals.

Answer 1

The Correct Option is B

Step 1: Use a standard integral.
This is a standard integral, and its value can be derived from integral tables or computed using substitution and symmetry.
Step 2: Conclusion.
Thus, the value of the integral is \( \frac{\pi}{4} \).
Final Answer: \[ \boxed{\frac{\pi}{4}} \]