University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 7 - Section 7.1 - The Logarithm Defined as an Integral - Exercises - Page 401: 1



Work Step by Step

Solve $\int_{-3}^{-2}\dfrac{dx}{x}$ $\int_{-3}^{-2}\dfrac{dx}{x}=[\ln |x|]_{-3}^{-2}$ This implies $[\ln |x|]_{-3}^{-2}=\ln |-2|-\ln |-3|$ $=\ln 2-\ln 3$ Use logarithmic properties, $\ln m-\ln n=\ln(\dfrac{m}{n})$, we have Hence, $\int_{-3}^{-2}\dfrac{dx}{x}=\ln(\dfrac{2}{3})$
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