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#76 2011-07-21 09:13:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,262

Re: Tricky integral of a rational function

Hi;

I will provide something in a few minutes.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#77 2011-07-21 09:17:22

Au101
Member
Registered: 2010-12-01
Posts: 353

Re: Tricky integral of a rational function

Oh of course - take your time - I hadn't meant for this thread to cause you - or anybody else - even more hard work.

Last edited by Au101 (2011-07-21 09:17:41)

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#78 2011-07-21 09:23:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,262

Re: Tricky integral of a rational function

Hi;

Now what you do is form a 6 x 6 set of simultaneous linear equations. This is done by substituting x = -3,-2,-1,0,1,2 in the above. That wipes out the x and you are left with:

Which is exactly what we expected.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#79 2011-07-21 09:35:29

Au101
Member
Registered: 2010-12-01
Posts: 353

Re: Tricky integral of a rational function

Oooh thanks bobbym that's perfect, my only question would be where we've accounted for the fact that the product of our denominators is four times the original denominator. I also wonder if it would be possible to tell that our numerators would be quadratics if we hadn't had the answer to begin with - more out of curiosity than anything else.

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#80 2011-07-21 09:38:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,262

Re: Tricky integral of a rational function

Hi;

to tell that our numerators would be quadratics

One way is to say the numerator is an 8th degree poly,  a quadratic times by a six degree
poly is an 8th degree poly.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#81 2011-07-21 09:56:46

Au101
Member
Registered: 2010-12-01
Posts: 353

Re: Tricky integral of a rational function

Oooh yes, that's very good smile - I'm still confused about that pesky four though

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#82 2011-07-21 10:00:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,262

Re: Tricky integral of a rational function

I think that is just some factor that Mathematica pulled out, for what reason... I do not know.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#83 2011-07-21 10:20:03

Au101
Member
Registered: 2010-12-01
Posts: 353

Re: Tricky integral of a rational function

Hmmm, yes I see, but ought we not account for it. I tried taking the four outside, although perhaps that was not correct. What I am interested in, though, is why we don't have to worry about it when computing a,b,c,d,e and f

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#84 2011-07-21 10:23:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,262

Re: Tricky integral of a rational function

Hi;

Because in the "fit" for the coefficients a,b,c,d,e,f it gets taken care of all by itself.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#85 2011-07-21 16:00:39

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Tricky integral of a rational function

Hi,

Shouldn't the partial fraction we expect be of the form:



"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#86 2011-07-21 16:25:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,262

Re: Tricky integral of a rational function

Hi gAr;

That is two quadratics for the numerators also. Because

That is why I went right to 2 quadratics in the numerators.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#87 2011-07-21 16:36:05

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Tricky integral of a rational function

Hi bobbym,

Oh, okay!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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