Calculus II for DUMmIES

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Calculus II
FOR
DUMmIES
‰
by Mark Zegarelli
Calculus II For Dummies
®
Published by
Wiley Publishing, Inc.
111 River St.
Hoboken, NJ 07030-5774
www.wiley.com
Copyright © 2008 by Wiley Publishing, Inc., Indianapolis, Indiana
Published simultaneously in Canada
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Library of Congress Control Number: 2008925786
ISBN: 978-0-470-22522-6
Manufactured in the United States of America
10 9 8 7 6 5 4 3 2 1
About the Author
Mark Zegarelli
is the author of
Logic For Dummies
(Wiley),
Basic Math &
Pre-Algebra For Dummies
(Wiley), and numerous books of puzzles. He holds
degrees in both English and math from Rutgers University, and lives in Long
Branch, New Jersey, and San Francisco, California.
Dedication
For my brilliant and beautiful sister, Tami. You are an inspiration.
Author’s Acknowledgments
Many thanks for the editorial guidance and wisdom of Lindsay Lefevere,
Stephen Clark, and Sarah Faulkner of Wiley Publishing. Thanks also to the
Technical Editor, Jeffrey A. Oaks, PhD. Thanks especially to my friend David
Nacin, PhD, for his shrewd guidance and technical assistance.
Much love and thanks to my family: Dr. Anthony and Christine Zegarelli,
Mary Lou and Alan Cary, Joe and Jasmine Cianflone, and Deseret Moctezuma-
Rackham and Janet Rackham. Thanksgiving is at my place this year!
And, as always, thank you to my partner, Mark Dembrowski, for your con-
stant wisdom, support, and love.
 Publisher’s Acknowledgments
We’re proud of this book; please send us your comments through our Dummies online registration
form located at www.dummies.com/register/.
Some of the people who helped bring this book to market include the following:
Acquisitions, Editorial, and Media
Development
Project Editor:
Stephen R. Clark
Acquisitions Editor:
Lindsay Sandman Lefevere
Senior Copy Editor:
Sarah Faulkner
Editorial Program Coordinator:
Erin Calligan Mooney
Technical Editor:
Jeffrey A. Oaks, PhD
Editorial Manager:
Christine Meloy Beck
Editorial Assistants:
Joe Niesen, David Lutton
Cover Photos:
Comstock
Cartoons:
Rich Tennant
(www.the5thwave.com)
Composition Services
Project Coordinator:
Katie Key
Layout and Graphics:
Carrie A. Cesavice
Proofreaders:
Laura Albert, Laura L. Bowman
Indexer:
Broccoli Information Management
Special Help
David Nacin, PhD
Publishing and Editorial for Consumer Dummies
Diane Graves Steele,
Vice President and Publisher, Consumer Dummies
Joyce Pepple,
Acquisitions Director, Consumer Dummies
Kristin A. Cocks,
Product Development Director, Consumer Dummies
Michael Spring,
Vice President and Publisher, Travel
Kelly Regan,
Editorial Director, Travel
Publishing for Technology Dummies
Andy Cummings,
Vice President and Publisher, Dummies Technology/General User
Composition Services
Gerry Fahey,
Vice President of Production Services
Debbie Stailey,
Director of Composition Services
 Contents at a Glance
Introduction .................................................................1
Part I: Introduction to Integration .................................9
Chapter 1: An Aerial View of the Area Problem ...........................................................11
Chapter 2: Dispelling Ghosts from the Past:
A Review of Pre-Calculus and Calculus I ....................................................................37
Chapter 3: From Definite to Indefinite: The Indefinite Integral ..................................73
Part II: Indefinite Integrals ......................................103
Chapter 4: Instant Integration: Just Add Water (And C) ...........................................105
Chapter 5: Making a Fast Switch: Variable Substitution ...........................................117
Chapter 6: Integration by Parts ...................................................................................135
Chapter 7: Trig Substitution: Knowing All the (Tri)Angles ......................................151
Chapter 8: When All Else Fails: Integration with Partial Fractions .........................173
Part III: Intermediate Integration Topics ....................195
Chapter 9: Forging into New Areas: Solving Area Problems ....................................197
Chapter 10: Pump up the Volume: Using Calculus to Solve 3-D Problems .............219
Part IV: Infinite Series .............................................241
Chapter 11: Following a Sequence, Winning the Series ............................................243
Chapter 12: Where Is This Going? Testing for Convergence and Divergence ........261
Chapter 13: Dressing up Functions with the Taylor Series ......................................283
Part V: Advanced Topics ...........................................305
Chapter 14: Multivariable Calculus .............................................................................307
Chapter 15: What’s So Different about Differential Equations? ...............................327
Part VI: The Part of Tens ..........................................341
Chapter 16: Ten “Aha!” Insights in Calculus II ............................................................343
Chapter 17: Ten Tips to Take to the Test ...................................................................349
Index .......................................................................353
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