Definite Integration Question 115
Question: $ \int_0^{1}{\frac{\log x}{\sqrt{1-x^{2}}}dx=} $
[BIT Ranchi 1984]
Options:
A) $ \frac{\pi }{2}\log 2 $
B) $ \pi \log 2 $
C) $ -\frac{\pi }{2}\log 2 $
D) $ -\pi \log 2 $
Show Answer
Answer:
Correct Answer: C
Solution:
Put $ x=\sin \theta , $ we get $ \int_0^{1}{\frac{\log x}{\sqrt{1-x^{2}}}dx=\int_0^{\pi /2}{\frac{\log \sin \theta .\cos \theta }{\cos \theta }}}d\theta $
$ =\int_0^{\pi /2}{\log \sin \theta }d\theta =-\frac{\pi }{2}\log 2 $ .
BETA
