Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 5 - Section 5.1 - Areas and Distances - 5.1 Exercises - Page 381: 4

Answer

a) 1.18347 b) 0.790766

Work Step by Step

a) $\Delta x=\frac{\frac{\pi}{2}-0}{4}=\frac{\pi}{8}$ $\sum_{i=0}^{3}\sin(\frac{\pi}{8}+\frac{\pi}{8}i)\frac{\pi}{8}=1.18347$ Because the function is concave down and right endpoints are used, the Riemann sum is an overestimate b) $\Delta x=\frac{\frac{\pi}{2}-0}{4}=\frac{\pi}{8}$ $\sum_{i=0}^{3}\sin(\frac{\pi}{8}i)\frac{\pi}{8}=0.790766$ Because the function is concave down and left endpoints are used, the Riemann sum is an underestimate
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