A) 2
B) 3
C) 4
D) 5
Correct Answer: A
Solution :
Required area \[=\int\limits_{-1}^{1}{\left( \frac{2}{1+{{x}^{2}}}-{{x}^{2}} \right)}\,dx=2\int\limits_{0}^{1}{\left( \frac{2}{1+{{x}^{2}}}-{{x}^{2}} \right)}\,dx\] \[=2\left( 2{{\tan }^{-1}}x-\frac{{{x}^{3}}}{3} \right)_{0}^{1}=2\left( \frac{\pi }{2}-\frac{1}{3} \right)=\pi -\frac{2}{3}\] \[\therefore \left[ \pi -\frac{2}{3} \right]=2\]You need to login to perform this action.
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