Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 4 - Applications of the Derivative - 4.9 Antiderivatives - 4.9 Exercises: 34

Answer

$$\frac{5}{7}{r^{7/5}} + C$$

Work Step by Step

$$\eqalign{ & \int {\root 5 \of {{r^2}} } dr \cr & {\text{then}} \cr & = \int {{r^{2/5}}} dr \cr & {\text{use power rule for indefinite integrals}} \cr & = \frac{{{r^{7/5}}}}{{7/5}} + C \cr & {\text{simplify}} \cr & = \frac{5}{7}{r^{7/5}} + C \cr & {\text{check by differentiation}} \cr & {\text{ = }}\frac{d}{{dr}}\left( {\frac{5}{7}{r^{7/5}} + C} \right) \cr & = \frac{5}{7}\left( {\frac{7}{5}} \right){r^{2/5}} + 0 \cr & = {r^{2/5}} \cr & = \root 5 \of {{r^2}} \cr} $$
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