University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises: 57

Answer

$\frac{-20}{3}$

Work Step by Step

We can calculate the area by integrating the function from -3 to 2. $\int_{-3}^{2} (-x^2-2x)dx =[\frac{-x^3}{3}-x^2]_{-3}^{2}=[\frac{-2^3}{3}-2^2]-[\frac{-(-3)^3}{3}-(-3)^2]=[\frac{-8}{3}-4]-[\frac{27}{3}-9]=[\frac{-20}{3}]-0=\frac{-20}{3}$
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