Question

Value of \( \displaystyle \int_{0}^{\pi/2} \dfrac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \) is:

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

Hint:

Exploit symmetry with complementary substitutions.

Answer 1

The Correct Option is C

Using \( x \rightarrow \dfrac{\pi}{2} - x \) and adding,
\( I = \dfrac{1}{2} \int_{0}^{\pi/2} dx = \dfrac{\pi}{4} \)