Definite Integration Question 116
Question: $ \int_0^{\pi /2}{x\cot xdx} $ equals
[RPET 1997]
Options:
A) $ -\frac{\pi }{2}\log 2 $
B) $ \frac{\pi }{2}\log 2 $
C) $ \pi \log 2 $
D) $ -\pi \log 2 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int_0^{\pi /2}{x\cot xdx} $
Integrating by parts, we get $ [x(\log \sin x)]_0^{\pi /2}-\int_0^{\pi /2}{\log \sin xdx} $
$ I=-( -\frac{\pi }{2}\log 2 )=\frac{\pi }{2}\log 2 $ .
BETA
