1. MTH 252 Integral Calculus Chapter 8 – Principles of Integral Evaluation Section 8.1 – An Overview of Integration Methods Copyright © 2005 by Ron Wallace, all rights reserved.

2. Four Approaches to Integration 1. Recognition  Review list on pages 511-512 2. Computer Algebra Systems (CAS)  Examples: Mathematica, Maple, Derive  Problems: Can’t solve some and others give unnecessary complicated answers. 3. Tables  See inside front & back covers  Problem: Not exhaustive 4. Transformation Methods  Change to something recognizable.  Examples: Substitution & Algebraic Equivalence  The topic of this chapter! Also, for definite integrals, numerical approximation methods.

3. Transformation Methods  Substitution  Integration by Parts  Trigonometric Integrals Powers of Trigonometric Functions  Trigonometric Substitutions  Partial Fractions All of these attempt to change the integral into something that can be integrated by recognition. Many problems will require the use of two or more of these methods!