A) 1
B) \[\frac{1}{\sqrt{3}}\]
C) \[\frac{1}{3}\]
D) None of these
Correct Answer: B
Solution :
The x-coordinate of A is \[\frac{1}{a}\] According to the given condition, \[1=\int_{0}^{1/a}{\left( \sqrt{\frac{x}{a}}-a{{x}^{2}} \right)}\text{ }dx\] Þ\[1=\frac{1}{\sqrt{a}}.\frac{2}{3}[{{x}^{3/2}}]_{0}^{1/a}-\frac{a}{3}[{{x}^{3}}]_{0}^{1/a}\]Þ \[{{a}^{2}}=\frac{1}{3}\Rightarrow a=\frac{1}{\sqrt{3}}\].You need to login to perform this action.
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