Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises - Page 407: 39

Answer

$8 + \ln 3$

Work Step by Step

$$\eqalign{ & \int_1^3 {\left( {2x + \frac{1}{x}} \right)} dx \cr & {\text{Integrate by using: }}\int {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C{\text{ and }}\int {\frac{1}{x}} dx = \ln \left| x \right| + C \cr & = \left[ {\frac{{2{x^2}}}{2} + \ln \left| x \right|} \right]_1^3 \cr & = \left[ {{x^2} + \ln \left| x \right|} \right]_1^3 \cr & {\text{Use The Fundamental Theorem of Calculus}},{\text{ Part 2}} \cr & = \left[ {{{\left( 3 \right)}^2} + \ln \left| 3 \right|} \right] - \left[ {{{\left( 1 \right)}^2} + \ln \left| 1 \right|} \right] \cr & {\text{Simplifying}} \cr & = \left( {9 + \ln 3} \right) - \left( {1 + 0} \right) \cr & = 8 + \ln 3 \cr} $$
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