Calculus II Workbook 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