Calculus II - Alyoops!

1 By Mark ZegarelliCalculus IIFORDUMmIES 4/30/08 11:54 PM Page iCalculus II For Dummies Published byWiley Publishing, River , NJ 2008 by Wiley Publishing, Inc., Indianapolis, IndianaPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system, or transmitted in any formor by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as per-mitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior writtenpermission of the Publisher, or authorization through payment of the appropriate per-copy fee to theCopyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400.

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5 Outside the at 317-572-3993, or fax technical support, please visit also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic of Congress Control Number: 2008925786 ISBN: 978-0-470-22522-6 Manufactured in the United States of America10 9 8 7 6 5 4 3 2 4/30/08 11:54 PM Page iiAbout the AuthorMark Zegarelliis the author of Logic For Dummies(Wiley), Basic Math & Pre-Algebra For Dummies (Wiley), and numerous books of puzzles. He holdsdegrees in both English and math from Rutgers University, and lives in LongBranch, New Jersey, and San Francisco, my brilliant and beautiful sister, Tami.

6 You are an s AcknowledgmentsMany thanks for the editorial guidance and wisdom of Lindsay Lefevere,Stephen Clark, and Sarah Faulkner of Wiley Publishing. Thanks also to theTechnical Editor, Jeffrey A. Oaks, PhD. Thanks especially to my friend DavidNacin, PhD, for his shrewd guidance and technical 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 4/30/08 11:54 PM Page iiiPublisher s AcknowledgmentsWe re proud of this book; please send us your comments through our Dummies online registrationform located at of the people who helped bring this book to market include the following:Acquisitions, Editorial, and MediaDevelopmentProject Editor: Stephen R.

7 ClarkAcquisitions Editor: Lindsay Sandman LefevereSenior Copy Editor: Sarah FaulknerEditorial Program Coordinator:Erin Calligan MooneyTechnical Editor: Jeffrey A. Oaks, PhDEditorial Manager: Christine Meloy BeckEditorial Assistants:Joe Niesen, David LuttonCover Photos: ComstockCartoons: Rich Tennant( )Composition ServicesProject Coordinator:Katie KeyLayout and Graphics:Carrie A. CesaviceProofreaders:Laura Albert, Laura L. Bowman Indexer:Broccoli Information ManagementSpecial HelpDavid Nacin, PhDPublishing and Editorial for Consumer DummiesDiane Graves Steele, Vice President and Publisher, Consumer DummiesJoyce Pepple, Acquisitions Director, Consumer DummiesKristin A.

8 Cocks, Product Development Director, Consumer DummiesMichael Spring, Vice President and Publisher, TravelKelly Regan,Editorial Director, TravelPublishing for Technology DummiesAndy Cummings,Vice President and Publisher, Dummies Technology/General UserComposition ServicesGerry Fahey,Vice President of Production ServicesDebbie Stailey,Director of Composition 4/30/08 11:54 PM Page ivContents at a GlanceIntroduction ..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.

9 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.

10 219 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 .. 4/30/08 11:54 PM Page vTable of ContentsIntroduction.