A) \[\frac{1}{\sqrt{3}}\]
B) \[\frac{1}{2}\]
C) 1
D) 1/3
Correct Answer: A
Solution :
Area enclosed between curves is OABCO. Thus, the point of intersection of y = ax2 and x = ay2 is given by\[x=a{{(a{{x}^{2}})}^{2}}\Rightarrow x=0,\frac{1}{a}\] \[\therefore \]Point of intersections are (0, 0) and \[\left( \frac{1}{a},\frac{1}{a} \right).\] Thus, required area OABCO \[\Rightarrow \]\[\int_{0}^{1/a}{\left( \sqrt{\frac{x}{a}}-a{{x}^{2}} \right)}dx=1\] (given) \[\Rightarrow \]\[{{\left[ \frac{1}{\sqrt{a}}.\frac{{{x}^{3/2}}}{3/2}-\frac{a{{x}^{3}}}{3} \right]}^{1/a}}=1\]\[\Rightarrow \]\[\frac{2}{3{{a}^{2}}}-\frac{1}{3{{a}^{2}}}=1\] \[\Rightarrow \]\[{{a}^{2}}=\frac{1}{3}\Rightarrow a=\frac{1}{\sqrt{3}}\] (as a > 0)You need to login to perform this action.
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