A) \[0\]
B) \[\pi \]
C) \[\frac{\pi }{2}\]
D) \[\frac{\pi }{4}\]
Correct Answer: A
Solution :
Let \[I=\int_{0}^{\pi /2}{\log \tan xdx}\] ...(i) \[I=\int_{0}^{\pi /2}{\log \tan \left( \frac{\pi }{2}-x \right)}dx\] \[\Rightarrow \] \[I=\int_{0}^{\pi /2}{\log \cot x}dx\] ?.(ii) On adding Eqs. (i) and (ii), \[2I=\int_{0}^{\pi /2}{\log (\tan x.\cot x)}dx\] \[=\int_{0}^{\pi /2}{\log (1)}dx\] \[\Rightarrow \] \[2I=0\] \[\Rightarrow \] \[I=0\]
You need to login to perform this action.
You will be redirected in
3 sec
