Question

If $\underset{0}{\overset{1}{\int }}\frac{\lambda nx}{\sqrt{1-x^2}}dx=k{\int }_0^{\pi }\ln (1+\cos x)dx$ then the value of $k$ is :

• A. 2
• B. $1/2$
• C. -2
• D. $-1/2$

Answer 1

Answer: (B)

Put $x=\sin \theta \Rightarrow$ L HS $=\underset{0}{\overset{\pi /2}{\int }}\ln (\sin \theta )d\theta =k\underset{0}{\overset{\pi }{\int }}\ln (1-\cos x)$
$=2k\underset{0}{\overset{\pi /2}{\int }}\ln (\sin x)dx\Rightarrow k=1/2$