Question

Evaluate the following definite integral:

${\int }_{\pi /6}^{\pi /4}\csc xdx$

Answer 1

$I={\int }_{\pi /6}^{\pi /4}\csc dx=\left[\log \right(\csc x-\cot x){]}_{\pi /6}^{\pi /4}=\log (\csc \frac{\pi }{4}-\cot \frac{\pi }{4})-\log (\csc \frac{\pi }{6}-\cot \frac{\pi }{6})$