7.5 Partial Fraction MethodFriday Jan 15

Do Now1) Evaluate

2) Combine fractions

Do Now

Partial Fraction Decomposition

• Partial Fraction Decomposition can be used to evaluate integrals by breaking up a fraction into several easier fractions

Proper rational functions

• A rational function is considered proper if the degree of the numerator is less than the degree of the denominator.

• Only proper rational functions can be decomposed into partial fractions

• If a rational function is not proper, it must be divided (long division)

Partial Fraction Decomposition

• 1) Factor the denominator into irreducible linear and quadratic factors

• 2) Break up the fraction by each denominator factor

• 3a) Assign each linear factor a variable constant• 3b) Assign each quadratic factor a variable linear

expression• 4) Combine each fraction together• 5) Set up a system of equations and solve

Ex – 2 partials

• Evaluate

Ex – 3 partials

• Evaluate

Ex – divide first

• Evaluate

Ex - repeated factor

• Evaluate

Ex – irreducible quadratic

• Evaluate

Closure

• Evaluate

• HW: p.434 #7 11 15 19 25 31 61 63