Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - 7.2 Substitution - 7.2 Exercises: 9

Answer

\[ =\dfrac{1}{12}(4z^2-5)^{3/2}+C \]

Work Step by Step

In order to integrate this function, we have to use a «u» substitution. Choose a u, derive it: $u = 4z^2-5 $ $du = 8zdz $ $\dfrac{1}{8}du=zdz $ Then substitute: \[ = \dfrac{1}{8}\int u^{1/2} du \] Then integrate \[ = \dfrac{1}{8} \bigg( \dfrac {2}{3}\bigg) u^{3/2}+C =\dfrac{1}{12}u^{3/2}+C \] And undo the substitution: \[ =\boxed{\dfrac{1}{12}(4z^2-5)^{3/2}+C} \]
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.