A) 0
B) 3
C) \[\frac{3{{\pi }^{2}}}{32}\]
D) \[\frac{3{{\pi }^{2}}}{16}\]
Correct Answer: C
Solution :
\[I=\int\limits_{0}^{3}{\frac{{{\tan }^{-1}}\{x\}}{1+{{\{x\}}^{2}}}dx}\] \[I=3\int\limits_{0}^{1}{\frac{{{\tan }^{-1}}x}{1+{{x}^{2}}}dx=\frac{3{{\pi }^{2}}}{32}}\]Ans.
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