A) \[(2\sqrt{2}-1)\]
B) \[\frac{1}{7}(2\sqrt{2}+1)\]
C) \[\frac{1}{7}(2\sqrt{2}-1)\]
D) None of these
Correct Answer: B
Solution :
\[{{A}_{1}}=2\int_{0}^{a}{\sqrt{4ax}}dx=4\sqrt{a}\int_{0}^{a}{\sqrt{x}}dx\] \[=4\sqrt{a}\frac{2}{3}[{{x}^{3/2}}]_{0}^{a}\] \[=\frac{8{{a}^{2}}}{3}\text{sq}\,\text{unit}\] and\[{{A}_{2}}=2\left[ \int_{a}^{2a}{\sqrt{4ax}}dx \right]\] \[=\frac{8\sqrt{a}}{3}[{{x}^{3/2}}]_{a}^{2a}\] \[=\frac{8\sqrt{a}}{3}[2\sqrt{2}-1]\]sq unit \[\therefore \]\[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{1}{2\sqrt{2}-1}=\frac{2\sqrt{2}+1}{7}\]You need to login to perform this action.
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