Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 107


$\ln 3. $

Work Step by Step

Using the fact that $\frac{u'}{u}=\ln u $, we have $$\int_4^{12} \frac{1}{x}dx =\ln x|_4^{12}=\ln 12-\ln 4=\ln \frac{12}{4}=\ln 3. $$ where used the property $\ln A-\ln B=\ln \frac{A}{B}.$
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