1. 7.5 Partial Fraction Method Friday Jan 15 Do Now 1)Evaluate 2)Combine fractions

2. Do Now

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

4. 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)

5. 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

6. Ex – 2 partials Evaluate

7. Ex – 3 partials Evaluate

8. Ex – divide first Evaluate

9. Ex - repeated factor Evaluate

10. Ex – irreducible quadratic Evaluate

11. Closure Evaluate HW: p.434 #7 11 15 19 25 31 61 63