anonymous
  • anonymous
Can someone explain me the steps of solving integrals using partial fractions?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Should i give you am example?
anonymous
  • anonymous
the integration is usually the easy part. finding the decomposition is a pain often
anonymous
  • anonymous
ya i don't get the steps. my book didnt tell me

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anonymous
  • anonymous
|dw:1326817894193:dw|
anonymous
  • anonymous
\[\frac{1}{(x-2)(x-3)}=\frac{a}{x-2}+\frac{b}{x-3}\] and you need a and b. we know that \[a(x-3)+b(x-2)=1\] so this is an easy one. since this equality has to be true for all values of x, it must be true if x = 2, so you get \[a(2-3)+b(2-2)=1\] \[-a=1\] \[a=-1\]
anonymous
  • anonymous
lol they got a diff answer is that ok?
anonymous
  • anonymous
How about using heavy side cover up for this one?
anonymous
  • anonymous
repeat the process making x = 3, and you will find \[b=1\] so we have \[\frac{1}{(x-2)(x-3)}=\frac{-1}{x-2}+\frac{1}{x-3}\] and now integrate term by term. now it is not ok
anonymous
  • anonymous
*no
anonymous
  • anonymous
They got 1/3 and -1/3
anonymous
  • anonymous
then maybe i made a mistake, let me write it out
TuringTest
  • TuringTest
is that a 5 on the second set of parentheses?
TuringTest
  • TuringTest
sat used a 3
anonymous
  • anonymous
doh, i used 3!!
anonymous
  • anonymous
LOL ya sorry abt that
anonymous
  • anonymous
ohhh didnt even notce that sat
TuringTest
  • TuringTest
sat has done it correctly for sure, just with the wrong number
anonymous
  • anonymous
no that is my fault, but idea is clear right?
anonymous
  • anonymous
\[a(x-5)+b(x-2)=1\] let \[x=2\] get \[-3a=1,x=-\frac{1}{3}\]
anonymous
  • anonymous
ummmm so y did u chose the value 2?
anonymous
  • anonymous
i am going to wager you can figure out why i picked 2
anonymous
  • anonymous
and what i will pick next also
anonymous
  • anonymous
need a hint?
anonymous
  • anonymous
well cuz it is in the denomanator? lol
anonymous
  • anonymous
i have this equality \[a(x-5)+b(x-2)=1\] and i am looking for a and b. so how can i find a easily?
anonymous
  • anonymous
by eliminating one variable by making one part =0
anonymous
  • anonymous
K i got that LOL
anonymous
  • anonymous
zactly. so first we let x =2, and then we let x = 5
anonymous
  • anonymous
oh ok got that :D Thanks :D
anonymous
  • anonymous
yw
anonymous
  • anonymous
I thought u guys started teaching today
anonymous
  • anonymous
This one a is a simple one if I have a more difficult one I will be back :D
anonymous
  • anonymous
with some practice you can do this: write \[\frac{1}{(x-2)(x-5)}=\frac{a}{x-2}+\frac{b}{x-5}\] now to find a, put your finger over the x - 2 in the first expression, put x = 2 and get \[a=\frac{1}{2-3}=-\frac{1}{3}\]
myininaya
  • myininaya
its called office hours
anonymous
  • anonymous
Thanks sat :D
anonymous
  • anonymous
i really need to get back to work, but i have 30 emails to send out and got bored bored bored. later
anonymous
  • anonymous
LOL bye

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