Integration Strategy

Author: John J Weber III, PhD Corresponding Textbook Sections:

• Section 7.5 – Strategy for Integration

Expected Educational Results

• Objective 08–01: I can identify the appropriate method to evaluate an integral.

Bloom’s Taxonomy

A modern version of Bloom’s Taxonomy is included here to recognize various different levels of understanding and to encourage you to work towards higher-order understanding (those at the top of the pyramid). All Objectives, Investigations, Activities, etc. are color-coded with the level of understanding.

Integration Strategy

This is a suggested strategy to use while attempting to evaluating an integral. This can be used for indefinite and definite integrals. After sufficient practice, you should be able to quickly identify the procedure necessary for a specific integral.

Note: Please see the corresponding Concept Module for the procedure to each strategy.

1. Use known formulas from your knowledge of derivatives

2. Use algebra to rewrite the integrand

3. u Substitution

4. Integration by parts

5. Trigonometric Integrals

6. Trigonometric substitution

7. Use the method of partial fractions

8. Use multiple methods

9. Use a Table of integrals

10. Use technology [Mathematica may result in a different form of the answer].

If at first you don't succeed, try again. Sometimes a combination of the above methods may be required. Most important of all, practice.

Homework

At this time, you should be able to complete the following assignments:

• Section 7.5: # 1–7, 11, 13, 16–21, 23, 25, 45, 49, 57, 67, 71, 77, 79, 81, 83.

CC BY-NC-SA 4.0

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

Last Modified: Monday, 6 September 2020 13:33 EDT