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: 23

Answer

$$\frac{{{x^6}}}{2} - \frac{{5{x^{10}}}}{2} + C$$

Work Step by Step

$$\eqalign{ & \int {\left( {3{x^5} - 5{x^9}} \right)} dx \cr & {\text{by the power rule for indefinite integrals}} \cr & {\text{ = }}\frac{{3{x^{5 + 1}}}}{{5 + 1}} - \frac{{5{x^{9 + 1}}}}{{9 + 1}} + C \cr & {\text{ = }}\frac{{3{x^6}}}{6} - \frac{{5{x^{10}}}}{{10}} + C \cr & {\text{ = }}\frac{{{x^6}}}{2} - \frac{{5{x^{10}}}}{2} + C \cr & \cr & \cr & {\text{check the antiderivative by differentiation}} \cr & {\text{ = }}\frac{d}{{dx}}\left( {\frac{{{x^6}}}{2} - \frac{{{x^{10}}}}{2} + C} \right) \cr & {\text{ = }}\frac{{6{x^5}}}{2} - \frac{{10{x^9}}}{2} + 0 \cr & {\text{simplify}} \cr & {\text{ = }}3{x^5} - 5{x^9} \cr} $$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.