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: 16

Answer

(a) $ 45 \frac{2}{3} km/h$ (b) $5.2s$

Work Step by Step

(a) $v_{ave} = \frac{1}{12} \int^{12}_0 v(t) dt = \frac{1}{12} I$ Use the Midpoint Rule with $n = 3$ and $\Delta t = 4$ to estimate I. $I \approx M_3 = 4[v(2) +v(6) +v(10)] = 4[21+50+66] = 548$. Thus, $v_{ave} \approx \frac{1}{12} \times 548 = 45 \frac{2}{3} km/h$ (b) Estimating from the graph, $v(t) = 45 \frac{2}{3}$ when $t \approx 5.2s$
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