Partial Fraction

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

• Section 7.4 – Integration of Rational Functions by Partial Fractions

Expected Educational Results

• Objective 06–01: I can use partial fractions to evaluate an indefinite integral.

• Objective 06–02: I can use partial fractions to evaluate a definite integral using FTC-II.

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.

Partial Fractions

Need for the Method of Partial Fractions

Investigation 01

Explain why $u$$u$-substitution is NOT a valid method for evaluating the following integrals:

1. ${\displaystyle \int \frac{3}{x^2+3x+2}dx}$$\displaystyle\int{\frac{3}{x^2+3x+2}\,dx}$

2. ${\displaystyle \int \frac{1}{x^3-4x}dx}$$\displaystyle\int{\frac{1}{x^3-4x}\,dx}$

3. ${\displaystyle \int \frac{x}{x^3-1}dx}$$\displaystyle\int{\frac{x}{x^3-1}\,dx}$

4. ${\displaystyle \int \frac{x+2}{x^2-2x+1}dx}$$\displaystyle\int{\frac{x+2}{x^2-2x+1}\,dx}$

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Created: Monday, 6 September 2020 13:33 EDT Last Modified: Wednesday, 08 September 2021 - 05:40 (EDT)