Question

Value of \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1 + \sqrt{\cot x}} dx \]

• A. \( \frac{\pi}{6} \)
• B. \( \frac{\pi}{12} \)
• C. 12
• D. None of these

Hint:

Simplifying the integrand using trigonometric identities helps in evaluating the integral.

Answer 1

The Correct Option is B

Use standard integration techniques and simplify the integral to find the value as \( \frac{\pi}{12} \).
Final Answer: \[ \boxed{\frac{\pi}{12}} \]