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: 11


(a) $$\frac{4}{\pi}$$ (b) $$c = c_1 \approx1.238 or c_2 \approx2.808$$

Work Step by Step

(a) $$f_{ave} = \frac{1}{\pi} \int^{\pi}_0 (2 sin x - sin 2x) dx$$ $$=\frac{1}{\pi} [-2 cos x + \frac{1}{2} cos 2x]^{\pi}_0$$ $$=\frac{1}{\pi} [(2+\frac{1}{2})-(-2+\frac{1}{2})] = \frac{4}{\pi}$$ (b) $$f(c) = f_{ave}, 2 sin c - sin 2c = \frac{4}{\pi}$$ $$c = c_1 \approx1.238 or c_2 \approx2.808$$
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