MATH 101 Lecture Notes - Lecture 16: Partial Fraction Decomposition
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Math 101 -lecture 16 - integration of partial fractions, wednesday february 11th. We begin with a review of long division. Recall how we divide integers for example , 12783/91. There is an analogous process to divide polynomials: for example ( x3 x+1 (x 6) partial fraction decomposition is a tool we use to clean up an integrand and make it more approachable. Using long division, we write f(x) as a sum of the polynomial and a rational g(x) function in which the degree of the numerator is strictly less than the degree of the denominator. 1: if we can write the denominator as a product of linear terms (i. e polynomials of the form ax+b) then the p. f. d is f(x)/(( a 1 x +b 1 (a 2 x+b 2) (a k x +b k) = A 1/(a 1 x+b 1)+ a 2/(a 2 x+b 2)+ a k/ . K divides the denominator then the p. f. d contains the terms.
