Calculus II For Dummies

The easy (okay, easier) way to master advanced calculus topics and theories

Calculus II For Dummies will help you get through your (notoriously difficult) calc class—or pass a standardized test like the MCAT with flying colors. Calculus is required for many majors, but not everyone’s a natural at it. This friendly book breaks down tricky concepts in plain English, in a way that you can understand. Practical examples and detailed walkthroughs help you manage differentiation, integration, and everything in between. You’ll refresh your knowledge of algebra, pre-calc and Calculus I topics, then move on to the more advanced stuff, with plenty of problem-solving tips along the way.

• Review Algebra, Pre-Calculus, and Calculus I concepts
• Make sense of complicated processes and equations
• Get clear explanations of how to use trigonometry functions
• Walk through practice examples to master Calc II

Use this essential resource as a supplement to your textbook or as refresher before taking a test—it’s packed with all the helpful knowledge you need to succeed in Calculus II.

Mark Zegarelli is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II Workbook For Dummies. Through online tutoring, he teaches mul­tiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com.

Introduction 1

Part 1: Introduction to Integration 7

Chapter 1: An Aerial View of the Area Problem 9

Chapter 2: Forgotten but Not Gone: Review of Algebra and Pre-Calculus 27

Chapter 3: Recent Memories: Review of Calculus I 53

Part 2: From Definite to Indefinite Integrals 73

Chapter 4: Approximating Area with Riemann Sums 75

Chapter 5: There Must Be a Better Way — Introducing the Indefinite Integral 87

Part 3: Evaluating Indefinite Integrals 103

Chapter 6: Instant Integration: Just Add Water (And C) 105

Chapter 7: Sharpening Your Integration Moves 117

Chapter 8: Here’s Looking at U-Substitution 141

Part 4: Advanced Integration Techniques 153

Chapter 9: Parting Ways: Integration by Parts 155

Chapter 10: Trig Substitution: Knowing All the (Tri)Angles 173

Chapter 11: Rational Solutions: Integration with Partial Fractions 197

Part 5: Applications of Integrals 219

Chapter 12: Forging into New Areas: Solving Area Problems 221

Chapter 13: Pump Up the Volume: Using Calculus to Solve 3-D Problems 243

Chapter 14: What’s So Different about Differential Equations? 265

Part 6: Infinite Series 275

Chapter 15: Following a Sequence, Winning the Series 277

Chapter 16: Where Is This Going? Testing for Convergence and Divergence 295

Chapter 17: Dressing Up Functions with the Taylor Series 319

Part 7: The Part of Tens 341

Chapter 18: Ten “Aha!” Insights in Calculus II 343

Chapter 19: Ten Tips to Take to the Test 351

Index 357

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