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Monday January 17
−
Lecture 6 :
Rational functions : Partial fractions
(
Refers to
Section 7.4 of your text
)
Expectations:
1.
Solve integrals containing rational functions by “partial fractions” method.
In this lecture we integrate rational functions where the degree of the numerator is less
than the degree of the denominator.
6.1
Rational functions as partial fractions
−
The method of integration called
Partial
fractions
is an algorithm for integrating a rational function where the degree of the
denominator is larger than the degree of the numerator. The principles of “partial
fractions” are given as we proceed through the following examples.
6.2
Example 1 : Case where
the irreducible factors of the denominator are all of degree 1.
Find
Solution:
Solve for
A
and
B
:
We now integrate:
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View Full Document6.2.1 Principle applied in example 1
:
If the irreducible factors in the denominator are all of degree 1 and of
multiplicity 1 then express the integrand as a sum of partial fractions each of
which has a constant as numerator.
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 Spring '07
 Anoymous
 Calculus, Fractions, Integrals, Rational Functions

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