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
