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Area of a Circle

The area in s...

Question

The area (in sq. units) of the region, given by the set ${(x, y) \in R \times R | x \geq 0, 2 x^{2} \leq y \leq 4 - 2 x}$ is

A

\frac{8}{3}

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B

\frac{7}{3}

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C

\frac{17}{3}

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D

\frac{13}{3}

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Solution

The correct option is B $\frac{7}{3}$

Area $A = \int_{0}^{1} ((4 - 2 x) - 2 x^{2}) d x$
$= {[4 x - x^{2} - \frac{2 x^{3}}{3}]}_{0}^{2} = 4 - 1 - \frac{2}{3} = \frac{7}{3}$

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