Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 5 - Applications of Integration - 5.5 Average Value of a Function - 5.5 Exercises - Page 391: 9

Answer

(a) $$1$$ (b) $$c = 2 or 4$$

Work Step by Step

(a) $$f_{ave} = {1\over 3} \int ^5 _2 (x-3)^2 dx = {1\over 3} [{1\over 3} (x-3)^3]^5 _2$$ $$={1\over 9} [2^3 - (-1)^3] = {1\over 9} (8+1) = 1$$ (b) $$f(c) = f_{ave}$$ $$(c-3)^2 = 1$$ $$c-3 = \pm1$$ $$c = 2 or 4$$
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.