A) \[\frac{4\pi }{3}-\sqrt{3}\]
B) \[\frac{8\pi }{3}-\sqrt{3}\]
C) \[\frac{4\pi }{3}+\sqrt{3}\]
D) \[\frac{5\pi }{3}+\sqrt{3}\]
Correct Answer: B
Solution :
Area of smaller part \[=2\,\int_{1}^{2}{\sqrt{4-{{x}^{2}}}}\,dx\] \[=2\,\left[ \frac{x}{2}\sqrt{4-{{x}^{2}}}+2{{\sin }^{-1}}\frac{x}{2} \right]_{1}^{2}\]\[=2\,\left[ 2.\frac{\pi }{2}-\left[ \frac{\sqrt{3}}{2}-2.\frac{\pi }{6} \right] \right]\] \[=2\,\left[ \pi -\left[ \frac{\sqrt{3}}{2}-\frac{\pi }{3} \right] \right]\]\[=\frac{8\pi }{3}-\sqrt{3}\].You need to login to perform this action.
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