4.3 Properties of the Definite Integral

Summary

By the end of your studying, you should know:

• How the definite integral relates to area.
• The relationship between the integral from a to b and the integral from b to a.
• How find the integral of an odd function over a symmetric interval.
• How find the integral of an even function over a symmetric interval.
• The Mean Value Theorem for Definite Integrals.
• What the average value of a function is.

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Examples Evaluate Write the expression as a definite integral. Evaluate Applets Mean Value Theorem for Integrals Videos See short videos of worked problems for this section. Quiz Take a quiz. Exercises See Exercises for 4.3 Properties of the Definite Integral (PDF). Work online to solve the exercises for this section, or for any other section of the textbook.

Resources on the Web Information on Newton Biographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics" Information on Leibniz Biographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics" Calculus Applications Project Intermath Properties of the Integral Visual Calculus

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4.2 The Definite Integral

Table of Contents

4.4 The Fundamental Theorem of Calculus

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel