Definite Integration Question 111
Question: $ \int_0^{1}{\log \sin ( \frac{\pi }{2}x )}dx= $
[RPET 1997]
Options:
A) $ -\log 2 $
B) $ \log 2 $
C) $ \frac{\pi }{2}\log 2 $
D) $ -\frac{\pi }{2}\log 2 $
Show Answer
Answer:
Correct Answer: A
Solution:
Put $ \frac{\pi }{2}x=\theta \Rightarrow dx=\frac{2}{\pi }d\theta $ ; As $ x=0 $ to $ 1, $
$ \theta =0 $ to $ \frac{\pi }{2} $
Then it reduces to $ \frac{2}{\pi }\int_0^{\pi /2}{\log \sin \theta d\theta =\frac{2}{\pi }[ -\frac{\pi }{2}\log 2 ]} $
$ =-\log 2 $ .
BETA
