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: 32

Answer

$$3{z^{4/3}} - \frac{3}{2}{z^{2/3}} + C$$

Work Step by Step

$$\eqalign{ & \int {\left( {4{z^{1/3}} - {z^{ - 1/3}}} \right)} dz \cr & {\text{use power rule for indefinite integrals}} \cr & = \frac{{4{z^{4/3}}}}{{4/3}} - \frac{{{z^{2/3}}}}{{2/3}} + C \cr & {\text{simplify}} \cr & = 3{z^{4/3}} - \frac{3}{2}{z^{2/3}} + C \cr & {\text{check by differentiation}} \cr & {\text{ = }}\frac{d}{{dz}}\left( {3{z^{4/3}} - \frac{3}{2}{z^{2/3}} + C} \right) \cr & = 3\left( {\frac{4}{3}} \right){z^{1/3}} - \frac{3}{2}\left( {\frac{2}{3}} \right){z^{ - 1/3}} + 0 \cr & = 4{z^{1/3}} - {z^{ - 1/3}} \cr} $$
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