Integration: Getting It All Together (UMAP)

These units teach a strategy for solving problems in integration that has three steps: simplify, classify, and modify. A chapter, including sample problems and solutions is devoted to each step of the procedure. Detailed solutions to chapter-end exercises are available in the separate Solutions Manual. Comparisons testing has shown the strategy taught by this unit to be unusually quick and effective.

Table of Contents:

INTRODUCTION
How to Use These Materials

1. SIMPLIFY!
1.1 Easy Algebraic Manipulations
1.2 Obvious Substitutions
Exercises for Chapter 1

2. CLASSIFY!
2.1 Rational Functions
Part 1: Basic rational functions
Part 2: Decomposing rational functions
2.2 Products
2.3 Trigonometric Functions
2.4 Special Functions
Exercises for Chapter 2

3. MODIFY!
3.1 Problem Similarities
3.2 Special Manipulations
A. Rationalizing denominators
B. Special use of trigonometic identities
C. Common denominator substitutions
D. Desperation substitutions
3.3 Need Analysis
Exercises for Chapter 3

APPENDIX I: PRE-TEST AND ANSWERS TO PRE-TEST

APPENDIX II: TABLE OF INTEGRALS

APPENDIX III: A DETAILED OUTLINE OF THE GENERAL PROCEDURE