A) \[\pi \]
B) \[2\pi \]
C) \[3\pi \]
D) None of these
Correct Answer: B
Solution :
\[I=\int_{-1}^{3}{\left\{ {{\tan }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right)+{{\tan }^{-1}}\left( \frac{{{x}^{2}}+1}{x} \right) \right\}}dx\] \[=\int_{-1}^{3}{\left\{ {{\tan }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right)+{{\cot }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right) \right\}}dx\] \[=\int_{-1}^{3}{\frac{\pi }{2}dx=}2\pi \].You need to login to perform this action.
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