The area of the region described by A = {(x, y): x2 + y2 ≤ 1 and y2 ≤ 1

Engineering

Mathematics

Introduction to Area

Question

The area of the region described by A = {(x, y): x² + y² ≤ 1 and y² ≤ 1 – x} is

$\frac{π}{2} + \frac{2}{3}$

$\frac{π}{2} + \frac{4}{3}$

$\frac{π}{2} - \frac{4}{3}$

$\frac{π}{2} - \frac{2}{3}$

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Shaded area = $\frac{π}{2} + 2 (\int_{0}^{1} \sqrt{1 - x} dx)$

$= \frac{π}{2} + 2 (\frac{2}{3}) = \frac{π}{2} + \frac{4}{3}$