Chapter 8 Integral Calculus and Its Uses

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

Section 8.2 Two-Dimensional Centers of Mass
8.2.1 An Example
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

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

Section 8.4 Applying Differentiation Rules to Integration
8.4.1 Algebraic Substitutions
8.4.2 Trigonometric Substitutions
8.4.3 Integration by Parts
8.4.4 Section Summary
Exercises

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

Chapter Summary
Chapter Review
Concepts and Applications
Formulas