Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.2 The Definite Integral - Preliminary Questions - Page 244: 2


(a) False. (b) True.

Work Step by Step

(a) False. It gives the "signed" area between the graph and the x-axis over the interval. In other words, if the function takes on negative values in the interval, these areas will be subtracted from the total. (b) True. Since the function is positive over the interval, none of the areas will be subtracted from the total. Thus the integral is equal to the geometric area.
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