Question

The integral \[ \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x + \cos x}}{\sin x + \cos x} \, dx \] is equal to

• A. 1
• B. \( \frac{\pi}{2} \)
• C. \( \frac{\pi}{4} \)
• D. \( \frac{\pi}{3} \)

Hint:

To solve integrals involving trigonometric functions, use appropriate trigonometric identities and substitution techniques.

Answer 1

The Correct Option is C

The given integral simplifies after substitution and integration, leading to the value \( \frac{\pi}{4} \).