A) \[\frac{\sqrt{3}}{4}-\frac{1}{3}\]
B) \[\frac{1}{3}+\frac{\sqrt{3}}{4}\]
C) \[\frac{1}{2}-\frac{\sqrt{3}}{4}\]
D) \[\frac{1}{2}+\frac{\sqrt{3}}{4}\]
Correct Answer: A
Solution :
Required Area = Area of the Region CMBC = Area of trapezium CLMBC - Area of the region CLMC \[=\int\limits_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}}{\left[ \left( 1-x \right)-{{\left( x-\frac{1}{2} \right)}^{2}} \right]}\,dx\] \[=\int\limits_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}}{\left( \frac{3}{4}-{{x}^{2}} \right)}\,dx\] \[=\left[ \frac{3}{4}x-\frac{{{x}^{3}}}{3} \right]_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}}\] \[=\frac{\sqrt{3}}{4}-\frac{1}{3}\]You need to login to perform this action.
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