Q. The value of the integral $\int_{0}^{\pi/2}{log|\tan{x|dx\ }is}$
A) $\pi\log 2$
B) 0
C) $- \pi\log 2$
D) None of these
Explanation
(b)
Let $I = \int_{0}^{\pi/2}{log|\tan{x|\ dx}}\$ …(i)
$\Rightarrow I = \int_{0}^{\pi/2}{\log\left| \tan\left( \frac{\pi}{2} - x \right) \right|}$ …(ii)
On adding Eqs. (i) and (ii), we get
$2I = \int_{0}^{\pi/2}{\log{|\tan{x\cot{x|\ dx}}}}$
$= \int_{0}^{\pi/2}{\log{1\ dx = 0}}$
$\Rightarrow I = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.