Volumes using integrals - Study guides, Class notes & Summaries

INTRODUCTION Dear Student Welcome to MAT2615. We trust that you will find the mathematics studied in this module interesting and useful, and that you will enjoy doing it. THIS TUTORIAL LETTER CONTAINS INFORMATION TO FACILITATE YOUR STUDIES. PLEASE READ IT CAREFULLY AND KEEP IT FOR FUTURE REFERENCE. The delivery mode for this module is “blended”, which means that only some study material will be printed and posted to you. All study material which may include additional material will be...

Functions 1 1.1 Functions and Their Graphs 1 1.2 Combining Functions; Shifting and Scaling Graphs 8 1.3 Trigonometric Functions 19 1.4 Graphing with Calculators and Computers 26 Practice Exercises 30 Additional and Advanced Exercises 38 2 Limits and Continuity 43 2.1 Rates of Change and Tangents to Curves 43 2.2 Limit of a Function and Limit Laws 46 2.3 The Precise Definition of a Limit 55 2.4 One-Sided Limits 63 2.5 Continuity 67 2.6 Limits Involving Infinity; Asymptotes of Graphs ...

Contents Preface vii Prerequisite Skills Diagnostic Test xix CHAPTER R Functions, Graphs, and Models 1 R.1 Graphs and Equations 2 R.2 Functions and Models 13 R.3 Finding Domain and Range 24 R.4 Slope and Linear Functions 33 R.5 Nonlinear Functions and Models 50 R.6 Mathematical Modeling and Curve Fitting 68 Chapter Summary 79 Chapter Review Exercises 85 Chapter Test 88 Extended Technology Application Average Price of a Movie Ticket 90 CHAPTER 1 Differentiation 93 1.1 Limits: A...

finding volume using integrals, cross sections, Cavalieri's Principle, volumes by cylindrical shells (not fully complete)

"Integration notes on Stuvia encompass comprehensive explanations and detailed examples of various integration techniques and applications. These notes are designed to aid students in understanding how to compute definite and indefinite integrals, using methods such as integration by parts, substitution, and special integration formulas. They often include step-by-step solutions to integration problems, covering topics like finding areas under curves, volumes of solids of revolution, and other ...

Practices problems and solutions that were covered in class

introduction 5 Chapter 1. Integrals 6 1.1. Areas and Distances. The Definite Integral 6 1.2. The Evaluation Theorem 11 1.3. The Fundamental Theorem of Calculus 14 1.4. The Substitution Rule 16 1.5. Integration by Parts 21 1.6. Trigonometric Integrals and Trigonometric Substitutions 26 1.7. Partial Fractions 32 1.8. Integration using Tables and CAS 39 1.9. Numerical Integration 41 1.10. Improper Integrals 46 Chapter 2. Applications of Integration 50 2.1. More about Areas 50 2.2. Vol...

Introduction Chapter 1. Integrals 6 1.1. Areas and Distances. The Definite Integral 6 1.2. The Evaluation Theorem 11 1.3. The Fundamental Theorem of Calculus 14 1.4. The Substitution Rule 16 1.5. Integration by Parts 21 1.6. Trigonometric Integrals and Trigonometric Substitutions 26 1.7. Partial Fractions 32 1.8. Integration using Tables and C A S 39 1.9. Numerical Integration 41 1.10. Improper Integrals 46 Chapter 2. Applications of Integration 50 2.1. More about Areas 50 2.2. Vo...

Topics for test 4: • Antiderivatives - Stewart 3.9 • Sigma notation - Stewart Appendix E • Areas and distances- Stewart 4.1 • The definite integral - Stewart 4.2 • The Fundamental Theorem of Calculus - Stewart 4.3 • Indefinite integrals and the net change theorem - Stewart 4.4 • The substitution rule - Stewart 4.5 • Integration by parts - Stewart 7.1 • Trigonometric integrals - Stewart 7.2 • Trigonometric substitution - Stewart 7.3 • Partial fractions - Stewart 7...