Question

\(\int_0^{\frac{\pi}{2}} \frac{dx}{\sqrt{\sin x + \cos x}} \)

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

Hint:

For integrals involving sums of trigonometric functions, consider symmetry or use standard reduction formulas for simplification.

Answer 1

The Correct Option is C

We are given: \[ I = \int_0^{\frac{\pi}{2}} \frac{dx}{\sqrt{\sin x + \cos x}} \] This integral is complex and requires a standard reduction formula or numerical evaluation. Upon evaluating, the answer is \( \frac{\pi}{2} \). Thus, the correct answer is \( \frac{\pi}{2} \).