Answer
$\dfrac{9}{2}$
Work Step by Step
The area $(A)$ can be calculated as:
$A=\int_{-2}^1 [(2-x^2)-(x)] \ dx \\= \int_{-2}^1 (2-x^2-x) \ dx \\=[2x-\dfrac{x^3}{3}-\dfrac{x^2}{2}]_{-2}^{1} \\=\dfrac{7}{6}+\dfrac{10}{3} \\=\dfrac{9}{2}$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 6 - Applications of the Integral - Chapter Review Exercises - Page 319: 2
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