The area (in sq. units) of the region described by {(x, y) : y2 ≤ 2x and y ≥ 4x

Engineering

Mathematics

Introduction to Area

Question

The area (in sq. units) of the region described by {(x, y) : y² ≤ 2x and y ≥ 4x – 1} is

$\frac{7}{32}$

$\frac{5}{64}$

$\frac{9}{32}$

$\frac{15}{64}$

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$Required area = \int_{- \frac{1}{2}}^{1} (\frac{y + 1}{4} - \frac{y^{2}}{2}) dy = \frac{9}{32} .$