Calculus II Workbook For Dummies

Description

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-calculusWork through practical examples for integration, differentiation, and beyondTest your knowledge with practice problems and online quizzes―and follow along with step-by-step solutionsGet 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. Title Page Copyright Page Table of Contents Introduction About This Book Foolish Assumptions Icons Used in This Book Beyond the Book Where to Go from Here Part 1 Introduction to Integration Chapter 1 An Aerial View of the Area Problem Measuring Area on the xy-Graph Defining Area Problems with the Definite Integral Calculating Area Defined by Functions and Curves on the xy-Graph Answers and Explanations Chapter 2 Forgotten but Not Gone: Review of Algebra and Pre-Calculus Fractions Factorials Negative and Fractional Exponents Simplifying Rational Functions Trigonometry Parent Functions Parent Function Transformations Sigma Notation for Series Answers and Explanations Chapter 3 Recent Memories: Calculus Review Evaluating Limits Derivatives of Common Functions and the Constant Multiple Rule The Power Rule The Sum Rule The Product Rule and Quotient Rule The Chain Rule Answers and Explanations Part 2 From Definite to Indefinite Integrals Chapter 4 Approximating Area with Riemann Sums Calculating Riemann Sums with Left and Right Rectangles Getting a Better Estimate with Midpoint Rectangles Improving Your Estimate with the Trapezoid Rule Using Simpson’s Rule to Further Improve Your Approximation Answers and Explanations Chapter 5 The Fundamental Theorem of Calculus and Indefinite Integrals Evaluating Definite Integrals Using FTC2 Anti-differentiation and Indefinite Integrals Signed and Unsigned Area Answers and Explanations Part 3 Evaluating Indefinite Integrals Chapter 6 Instant Integration Antiderivatives of Common Functions and the Constant Multiple Rule The Power Rule The Sum Rule Answers and Explanations Chapter 7 Sharpening Your Integration Moves Integrating Rational and Radical Functions Using Algebra to Prepare Functions for Integration Integrating Using Inverse Trig Functions Using Trig Identities to Prepare Functions for Integration Integrating Compositions of Functions with Linear Inputs Answers and Explanations Chapter 8 Here’s Looking at u-Substitution Understanding the How of u-Substitution When to Use u-Sub: The Simpler Case When to Use u-Sub: The More Complex Case Using Variable Substitution with Definite Integrals Answers and Explanations Part 4 Advanced Integration Techniques Chapter 9 Integration by Parts Using the Formula for Integration by Parts Knowing How to Assign u and dv Applying Integration by Parts More Than Once Answers and Explanations Chapter 10 Trig Substitution Integrating the Six Basic Trig Functions Integrating Powers of Sines and Cosines Integrating Powers of Tangents and Secants Using Trig Substitution Answers and Explanations Chapter 11 Integration with Partial Fractions Understanding Partial Fractions Integrating Case 1: Rational Expressions That Have Distinct Linear Factors Integrating Case 2: Repeated Linear Factors Integrating Case 3: Distinct Quadratic or Higher-Degree Factors Integrating Case 4: Repeated Quadratic Factors Answers and Explanations Part 5 Applications of Integrals Chapter 12 Solving Area Problems Breaking Definite Integrals in Two Looking at Improper Integrals Finding the Unsigned Area between Curves Using the Mean Value Formula for Integration Calculating Arclength Answers and Explanations Chapter 13 Pump up the Volume — Solving 3-D Problems Using Disk and Washer Methods to Find the Volume of Revolution around a Horizontal Axis Using Inverse Functions to Find Volume of Revolution around a Vertical Axis Surface Area of Revolution Shell Method Answers and Explanations Chapter 14 Differential Equations Understanding Differential Equations Solving Separable Differential Equations Answers and Explanations Part 6 Infinite Series Chapter 15 Sequences and Series Understanding Sequences Understanding Series Finding the Sequence of Partial Sums for a Series Understanding and Evaluating Geometric Series Understanding p-series Answers and Explanations Chapter 16 Convergent and Divergent Series Nth-Term Test for Divergence The Direct Comparison Test The Limit Comparison Test Integral Test Ratio Test Root Test Answers and Explanations Chapter 17 Taylor and Maclaurin Series Expressing Functions as Maclaurin Series Expressing Functions as Taylor Series Answers and Explanations Part 7 The Part of Tens Chapter 18 Ten Mathematicians Who Anticipated Calculus before Newton and Leibniz Zeno of Elea (495–430 BCE) Eudoxus of Cnidus (408–355 BCE) Archimedes (287–212 BCE) Lui Hui (3rd Century CE) Zu Chongzhi (425–500) Hasan Ibn al-Haytham (965–1040) Madhava of Sangamagrama (1340–1425) Johannes Kepler (1571–1630) Bonaventura Cavalieri (1598–1647) Isaac Barrow (1630–1677) Chapter 19 10 Skills from Pre-Calculus and Calculus I That Will Help You to Do Well in Calculus II Expressing Functions as Exponents Whenever Possible Knowing the Basic Trig Identities Cold Recalling the Most Common Functions and Their Basic Transformations Using Sigma Notation for Series Evaluating Limits Differentiating the Most Common Functions Knowing the Power Rule for Differentiation Applying the Product Rule Using the Chain Rule Calculating Common Derivatives Quickly in Your Head Index EULA