Calculus 8th Edition

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

Chapter 7 - Techniques of Integration - Review - True-False Quiz: 8

Answer

False

Work Step by Step

The Midpoint rule is not always more accurate than the Trapezoid rule. For example, make a function which is linear except it has narrow spikes at the midpoints of the subdivided intervals. Then the approximating rectangles for the midpoint rule will rise up to the level of the spikes, and be a huge overestimate. The trapezoid rule will basically not count the spikes. Hence, the given statement is false.
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