Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.4 The Fundamental Theorem of Calculus, Part I - Exercises - Page 258: 33



Work Step by Step

We have $$ \int_{-2}^{1}|x| d x= \int_{-2}^{0}|x| d x+ \int_{0}^{1}|x| d x\\ = -\int_{-2}^{0}xd x+ \int_{0}^{1}x d x =-\frac{1}{2}x^2|_{-2}^0+\frac{1}{2}x^2|_{0}^1\\ =-\frac{1}{2}(0-4)+\frac{1}{2}=\frac{5}{2}. $$
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