Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Practice Exercises - Page 439: 51

Answer

$$3\ln 7$$

Work Step by Step

$$\eqalign{ & \int_1^7 {\frac{3}{x}} dx \cr & = 3\int_1^7 {\frac{1}{x}} dx \cr & {\text{integrate using }}\int {\frac{1}{x}} dx = \ln \left| x \right| + C \cr & = 3\left( {\ln \left| x \right|} \right)_1^7 \cr & {\text{use the fundamental theorem of calculus }}\int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\,\,\left( {{\text{see page 281}}} \right) \cr & = 3\left( {\ln \left| 7 \right| - \ln \left| 1 \right|} \right) \cr & = 3\ln 7 \cr} $$
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