Question

Evaluate the definite integral: \[ \int_{\frac{\pi}{12}}^{\frac{5\pi}{12}} \frac{1}{1 + \sqrt{\cot x}} \, dx \]

Hint:

Whenever a definite integral contains symmetric limits such that \(a+b = \frac{\pi}{2}\) along with combinations of \(\sin x\)/\(\cos x\) or \(\tan x\)/\(\cot x\), the total integral value almost always evaluates simply to \(\frac{b-a}{2}\).

Answer 1