A) \[4\pi \] square units
B) \[2\pi \] square units
C) \[4{{\pi }^{2}}\] square units
D) 4 square units
Correct Answer: B
Solution :
[b] Given equation of circle is \[{{x}^{2}}+{{y}^{2}}=2\] \[\Rightarrow y=\sqrt{2-{{x}^{2}}}\] Required area \[=4\times \] Area of shaded portion \[=4\int_{0}^{\sqrt{2}}{\sqrt{2-{{x}^{2}}}dx}\] \[=4\left[ \frac{x}{2}\sqrt{2-{{x}^{2}}}+\frac{2}{2}{{\sin }^{-1}}\frac{x}{\sqrt{2}} \right]_{0}^{\sqrt{2}}\] \[=4\left[ {{\sin }^{-1}}\frac{\sqrt{2}}{\sqrt{2}} \right]=4{{\sin }^{-1}}1=4\times \frac{\pi }{2}=2\pi \,sq.\,\,unit.\]You need to login to perform this action.
You will be redirected in
3 sec