A) \[2\pi \]
B) \[\pi \]
C) \[\frac{21}{5}\pi \]
D) \[\frac{\pi }{4}\]
Correct Answer: A
Solution :
\[I=\int_{-1}^{3}{\left[ {{\tan }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right)+{{\cot }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right) \right]\,dx}\] \[=\int_{-1}^{3}{\left( \frac{\pi }{2} \right)\,dx=\left[ \frac{\pi \,x}{2} \right]_{-1}^{3}=2\pi }\], \[\left( \because {{\tan }^{-1}}(x)+{{\cot }^{-1}}(x)=\frac{\pi }{2} \right)\].
You need to login to perform this action.
You will be redirected in
3 sec
