4.5 Techniques of Integration

Summary

By the end of your studying, you should know:

• How to use differentials (introduced in 3.1).
• The method of substitution for indefinite and definite integrals.
• How to apply the integration by parts formula to indefinite and definite integrals.

Examples Find Use integration by parts to find an expression for taking u = (sin(x))4 and dv = sin(x) dx. Find Videos See short videos of worked problems for this section. Quiz Take a quiz. Exercises See Exercises for 4.5 Techniques of Integration (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 Substitution Visual Calculus Kouba Integration by Parts Visual Calculus Kouba

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4.4 The Fundamental Theorem of Calculus

Table of Contents

4.6 Trapezoid Rule

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