Chapter 8 Integral Calculus and Its Uses

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