The area bounded between the parabolas x^{2} = \frac{y}{4} \textrm{ }\textrm{ } and \textrm{ }\textrm{ } x^{2} = 9 y, and the straight line y = 2 is :

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Mathematics

Introduction to Area

Question

The area bounded between the parabolas $x^{2} = \frac{y}{4} and x^{2} = 9 y$ , and the straight line y = 2 is :

$10 \sqrt{2}$

$20 \sqrt{2}$

$\frac{20 \sqrt{2}}{3}$

$\frac{10 \sqrt{2}}{3}$

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$∴ Area = 2 \int_{0}^{2} (\sqrt{9 y} - \sqrt{\frac{y}{4}}) dy = \frac{20 \sqrt{2}}{3}$

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