Integration_of_Rational_Functions_by_Partial_Fraction.ppt

1
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
Rational function
Example
Example
Find
Find
Example
Find
Example
Example
Find
Find
2
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
3
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
4
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
5
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
Example
Multiply by
1
subsitute
subsitute
Match coeff
2
3
The Heaviside Cover-up
subsitute
6
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
1
Use long division
2
Check if we can use subsitution
3
Factor q(x) as linear factors or irreducible
quadratic
Express p(x)/q(x) as a sum of partial fraction
4
q(x) product of linear factor
q(x) product of quadratic (irred)
All distinct
Some repeated
repeated
All distinct
case1
case2
case3
case4
7
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
q(x) product of linear factor
Example
Find
All distinct
Some repeated
case1
case2
Example
Find
8
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
q(x) product of linear factor
All distinct
Some repeated
case1
case2
Example
Example
Find
9
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
q(x) product of quadratic (irred)
repeated
All distinct
case3
case4
Example
Example
10
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
q(x) product of quadratic (irred)
Example
repeated
Find
All distinct
case3
case4
Example
Expand by partial fraction
Example
Find
11
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
12
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
TERM-101
Solution
13
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
14
INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL
FRACTIONS
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)