MAC 2312 Lecture Notes - Lecture 6: Lego Mindstorms, Partial Fraction Decomposition
20 Jun 2018
School
Department
Course
Professor
Integration Of Rational Functions by partial Fraction TUESDAY
.June 5th
*Follow this method
,not book
example
g×3÷×d×
-partial Fraction
)×(¥ ,
=¥+13×1,4 ,
with A,B ,
c = cost
=A(x2+1 )+(B×+ c) X-7 must =\
⇐
2+1 )
=1= A(×2+1 )+(Bx + c) ×Identity Valid for every ×
1=(At
B) ×2 + Cx +A
Let x=o =>A = 1
"
r"
Compare the Coefficients of
→
×
"XAt B.
-0
a11
0=C ×c= o
At 13=0 =) -1 -B' '
,
"
A =
of
¥dx + fBE dx
×2+1
=Alnlxl +BS
,€ ,
+ of ¥,
=Ainlxl + If ,f÷, ,
+CS ×¥ ,
= AIn 1×1 +Bz In (1-2+1) +C+ an
''
×+Const
.
Proper fraction if
,
ABxtc
-
-A,B ,C= Constant
×-a
,×2+a2
Integration Of Rational Functions by partial fraction TUESDAY
.June 5. 1h
In general Rg{# ,Q(×),
RCx)-
polynomials
case 1Qcx ) =(a,× + b,).
..(an X + bn )
If degc Rcx ))<deg (QCx))
Rcx )A
,
An
partial Fraction =7-=-+
. • •
+-
QCX )a,xtb ,anxtbn
X3+× R ( ×)= ×3+ ×R'
C×)=3
Example :f-dx '
X-1QC×)= X-1
,Q'( ×)=1
Soln :1we do division
×2+ × + 2
x. i.×3t
×
-
×
3
-×2
-×+ ×
-
×
2
-x
.
Z X
2×-22
×3+x
-= × 2+1-+2 +
2-
×-l×-I
2fx2+x+z +S÷
=×z-3 +×÷ +2×+214×-11 + C
