A) \[\frac{3}{4}\]
B) \[\frac{3}{5}\]
C) \[\frac{5}{6}\]
D) \[\frac{2}{3}\]
Correct Answer: A
Solution :
Area of curve \[OAB=\int\limits_{a}^{{{a}^{2}}}{xdy}=2\int\limits_{a}^{{{a}^{2}}}{\sqrt{y}}dy=\frac{4}{3}({{a}^{3}})\] Also, area of \[\Delta OAB=\frac{1}{2}(2a)({{a}^{2}})={{a}^{3}}\] \[\therefore \frac{\text{area}\,\,\text{of}\,\,\Delta \text{OAB}}{\text{area}\,\,\text{of}\,\,\text{curve}\,\,\text{OAB}}\text{=}\frac{{{\text{a}}^{\text{3}}}}{\frac{\text{4}}{\text{3}}{{\text{a}}^{\text{3}}}}\text{=}\frac{\text{3}}{\text{4}}\]
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