Question

\( \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1+\sqrt{\tan x}}\,dx = \)

• A. \( \frac{\pi}{3} \)
• B. \( \frac{\pi}{6} \)
• C. \( \frac{\pi}{12} \)
• D. \( \frac{\pi}{2} \)

Hint:

For definite integrals with limits whose sum is \( \frac{\pi}{2} \), use \( x \to \frac{\pi}{2}-x \)This often converts \( \tan x \) into \( \cot x \) and simplifies the integral.

Answer 1

The Correct Option is C