Calculus II Workbook For Dummies

Work your way through Calc 2 with crystal clear explanations and tons of practice

Calculus II Workbook For Dummies is a hands-on guide to help you practice your way to a greater understanding of Calculus II. You’ll get tons of chances to work on intermediate calculus topics such as substitution, integration techniques and when to use them, approximate integration, and improper integrals. This book is packed with practical examples, plenty of practice problems, and access to online quizzes so you’ll be ready when it’s test time. Plus, every practice problem in the book and online has a complete, step-by-step answer explanation. Great as a supplement to your textbook or a refresher before taking a standardized test like the MCAT, this Dummies workbook has what you need to succeed in this notoriously difficult subject.

• Review important concepts from Calculus I and pre-calculus
• Work through practical examples for integration, differentiation, and beyond
• Test your knowledge with practice problems and online quizzes—and follow along with step-by-step solutions
• Get the best grade you can on your Calculus II exam

Calculus II Workbook For Dummies is an essential resource for students, alone or in tandem with Calculus II For Dummies.

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 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 3

Chapter 1: An Aerial View of the Area Problem 5

Chapter 2: Forgotten but Not Gone: Review of Algebra and Pre-Calculus 15

Chapter 3: Recent Memories: Calculus Review 37

Part 2: From Definite to Indefinite Integrals 51

Chapter 4: Approximating Area with Riemann Sums 53

Chapter 5: The Fundamental Theorem of Calculus and Indefinite Integrals 69

Part 3: Evaluating Indefinite Integrals 81

Chapter 6: Instant Integration 83

Chapter 7: Sharpening Your Integration Moves 91

Chapter 8: Here’s Looking at u-Substitution 103

Part 4: Advanced Integration Techniques 115

Chapter 9: Integration by Parts 117

Chapter 10: Trig Substitution 131

Chapter 11: Integration with Partial Fractions 151

Part 5: Applications of Integrals 167

Chapter 12: Solving Area Problems 169

Chapter 13: Pump up the Volume — Solving 3-D Problems 189

Chapter 14: Differential Equations 211

Part 6: Infinite Series 219

Chapter 15: Sequences and Series 221

Chapter 16: Convergent and Divergent Series 235

Chapter 17: Taylor and Maclaurin Series 255

Part 7: The Part of Tens 267

Chapter 18: Ten Mathematicians Who Anticipated Calculus before Newton and Leibniz 269

Chapter 19: 10 Skills from Pre-Calculus and Calculus I That Will Help You to Do Well in Calculus II 273

Index 279

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