A) \[\frac{5\sqrt{2}}{3}\text{sq}\text{.}\,\text{units}\]
B) \[\frac{10\sqrt{2}}{3}\text{sq}\text{.}\,\text{units}\]
C) \[\frac{15\sqrt{2}}{3}\text{sq}\text{.}\,\text{units}\]
D) \[\frac{20\sqrt{2}}{3}\text{sq}\text{.}\,\text{units}\]
Correct Answer: D
Solution :
[d]: Given, \[y=4{{x}^{2}}\]\[\Rightarrow {{x}^{2}}=\frac{y}{4}\] ...(i) \[{{x}^{2}}=9y\] ...(ii) and \[y=2\] ...(iii) \[\therefore \]Area bounded by the above three curves \[=2\int\limits_{0}^{2}{\left( 3\sqrt{y}-\frac{\sqrt{y}}{2} \right)dy=2\int\limits_{0}^{2}{\frac{5}{2}}\sqrt{y}dy=2\times \frac{5}{2}\left[ \frac{2{{y}^{3/2}}}{3} \right]_{0}^{2}}\]\[=\frac{10}{3}[2\sqrt{2}-0]=\frac{20\sqrt{2}}{3}\]sq. unitYou need to login to perform this action.
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