1/19/2009

• Integration by Partial Fractions: Section 8.2
• Some basic definitions

1. rational function

2. proper/improper rational functions

3. irreducible polynomial

• Review of Algebra skills that we’ll need

1. factoring/expanding

2. completing the square

3. solving a simple system of equations

4. simplifying polynomials and rational functions

5. dividing polynomials using (Euclidean) long division

• The Method of Partial Fractions
  Preliminary steps:
  i. If r(x) is an improper function…
  ii. Factor (if possible)
  iii. Simplify (if possible)
  PAUSE
  Method of Partial Fractions:

1. Rewrite r(x) in terms of its partial fractions.

2. Isolate the numerators.

3. Find the values of A and B that solve the equation.

i. Method 1: Collect like powers of x and match to coefficients on the left side. Solve the system.

ii. Method 2: Pick values of x that will simplify the equation in #2.

4. Rewrite the original in terms of the partial fractions. Solve.

• Examples

Practice Problems: Section 8.2: #1, 5, 15, 17, 31, 35

Reading Assignment: Please re-read Section 8.2 for class on Wednesday.

We will have our first quiz on Wednesday.