- Index
-
About this Chapter
- Section 8.1 Moments and Centers of Mass
- 8.1.1 Balancing a pool cue
- 8.1.2 Moments and Moment Arms
- 8.1.3 Center of Mass
- 8.1.4 Calculation of Mass
- 8.1.5 Calculation of Moment
- Section Summary
- Exercises
- Problems
- Section 8.2 Two-Dimensional Centers of Mass
- 8.2.1 An Aircraft Mobile
- 8.2.2 Calculation of Mass
- 8.2.3 Calculation of the Horizontal Moment
- 8.2.4 Calculation of \(\bar{x}\)
- 8.2.5 Calculation of the Vertical Moment and \(\bar{y}\)
- Section Summary
- Exercises
- Problems
- Section 8.3 Numerical Approximation of Integrals
- 8.3.1 Left-Hand and Right-Hand Sums
- 8.3.2 The Midpoint and Trapezoidal Rules
- 8.3.3 Simpson's Rule
- Section Summary
- Exercises
- Problems
- Section 8.4 Applying Differentiation Rules to Integration
- 8.4.1 Algebraic Substitutions
- 8.4.2 Trigonometric Substitutions
- 8.4.3 Integration by Parts
- Section Summary
- Exercises
- Problems
- Section 8.5 Representation of Periodic Functions
- 8.5.1 Building Complicated Waveforms from Sines and Cosines
- 8.5.2 Using Integrals to Analyze Waveforms
- Section Summary
- Exercises
- Problems
- Section 8.6 Using a Computer Algebra System to Integrate
- 8.6.1 Why Not Let the Computer Do It?
- 8.6.2 Integrating Rational Functions
- 8.6.3 Integrating Fractional Powers
- 8.6.4 Beyond Integration by Parts
- 8.6.5 What Can Go Wrong?
- 8.6.6 Different Answers to the Same Problem
- Section Summary
- Exercises
- Problems
- Chapter Summary
- Chapter Review
- Concepts and Applications
- Formulas
- Project 1. Length of a Curve