The area (in sq. units) of the region A = {(x, y) : x2 ≤ y ≤ x + 2} is

Engineering

Mathematics

Introduction to Area

Question

The area (in sq. units) of the region A = {(x, y) : x² ≤ y ≤ x + 2} is

$\frac{31}{6}$

$\frac{10}{3}$

$\frac{9}{2}$

$\frac{13}{6}$

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$x^{2} \leq y \leq x + 2$

x² = y; y = x + 2

x² = x + 2

x² – x – 2 = 0

(x – 2)(x – 1) = 0

x = 2, – 1