A) \[-\frac{\pi }{2}\ln \pi \]
B) 0
C) \[\frac{\pi }{2}\ln 2\]
D) none of these
Correct Answer: A
Solution :
[a] \[\int\limits_{0}^{\infty }{\left( \frac{\pi }{1+{{\pi }^{2}}{{x}^{2}}}-\frac{1}{1+{{x}^{2}}} \right)\log xdx}\] \[=\int\limits_{0}^{\infty }{\frac{\log \left( \frac{y}{\pi } \right)dy}{1+{{y}^{2}}}=\int\limits_{0}^{\infty }{\frac{\log x}{1+{{x}^{2}}}dx}}\] \[=-\int\limits_{0}^{\infty }{\frac{\log \pi }{1+{{y}^{2}}}dy=-\frac{\pi }{2}In\pi }\]
You need to login to perform this action.
You will be redirected in
3 sec
