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#1 2015-08-16 04:09:05
Why isn't the Feynman Integration Trick Working?
Why do I get different results from M for these two integrals? How do I solve the second one?
Last edited by Agnishom (2015-08-16 04:09:42)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#2 2015-08-16 09:33:57
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Why isn't the Feynman Integration Trick Working?
Do you know how to differentiate under the integral?
For the second integral, it is fun to use EM on it:
What did you try? IBP, contour integration, table lookup?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2015-08-16 12:21:42
Re: Why isn't the Feynman Integration Trick Working?
I tried differentiating under the integral
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#4 2015-08-16 13:13:03
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Why isn't the Feynman Integration Trick Working?
Please show what you did.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2015-08-16 21:03:11
Re: Why isn't the Feynman Integration Trick Working?
I got the first integral in post #1
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#6 2015-08-16 21:13:00
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Why isn't the Feynman Integration Trick Working?
What did you try to do?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2015-08-16 21:30:13
Re: Why isn't the Feynman Integration Trick Working?
I introduced a b in the numerator, as in log(bx)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#8 2015-08-16 21:50:52
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Why isn't the Feynman Integration Trick Working?
If I do not see your full workings how can I comment on where you went wrong.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2015-09-16 01:07:21
Re: Why isn't the Feynman Integration Trick Working?
Hurray!
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#11 2015-09-16 02:01:44
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Why isn't the Feynman Integration Trick Working?
But remember, Feynman did not know how to use contour integration.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#12 2015-09-16 02:08:35
Re: Why isn't the Feynman Integration Trick Working?
Neither do I
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#13 2015-09-16 02:11:08
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Why isn't the Feynman Integration Trick Working?
I am not that good in it either but then why not ask a question about it? Why ask about Feynman Integration?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2015-09-16 12:02:43
Re: Why isn't the Feynman Integration Trick Working?
I am not sure what you mean
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#15 2015-09-16 12:11:54
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Why isn't the Feynman Integration Trick Working?
Feynman integration is something other than contour integration. It would have been quicker to have asked for any way to solve the integral.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#16 2015-09-16 12:13:58
Re: Why isn't the Feynman Integration Trick Working?
Hm, tell me about Contour Integral
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#17 2015-09-16 12:21:28
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Why isn't the Feynman Integration Trick Working?
The second one is usually done in that way. zetafunc is preparing something, I would have to check my notes. I am already looking at the Feynman method again.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#18 2015-09-16 23:03:05
Re: Why isn't the Feynman Integration Trick Working?
I think I will instead upload a series of videos using contour integration, near the end of which I'll tackle Agnishom's problem. I'll start with some simpler examples, so you can get a feel for the residue theorem and the estimation lemma, before talking about the log integral.
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#19 2015-09-17 02:04:16
Re: Why isn't the Feynman Integration Trick Working?
It's a simple example, and one that can easily be done in more elementary ways, but I figured it would be easier to start with one of the easier problems before moving on to the harder ones.
Part 2, where I evaluate using methods of contour integration, is available here: https://www.youtube.com/watch?v=gYHNplUnGCkAnd here's Part 3, where I evaluate .Last edited by zetafunc (2015-09-18 04:18:38)
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#20 2015-09-18 00:02:55
Re: Why isn't the Feynman Integration Trick Working?
Hi zetafunc;
Thanks for the video. 
Unfortunately most of the idea dodged above my head. Can you do a video explaining contour integrals for a complete beginner to the technique?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#21 2015-09-18 00:55:59
Re: Why isn't the Feynman Integration Trick Working?
Sure. The main things you need to know to do definite integrals using methods of contour integration are:
-Which contour to use, and how to parametrise it;
-Defining your function (this is especially important for logarithms);
-Finding the poles of a function;
-Calculating residues at poles and using the residue theorem;
-Using the estimation lemma to bound curves that you want to tend to zero.
I'll try to create some videos about each of these things, summarising some of the concepts with some examples.
Last edited by zetafunc (2015-09-18 00:56:23)
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#22 2015-09-18 02:45:30
Re: Why isn't the Feynman Integration Trick Working?
Unfortunately, I do not know what a contour or pole is. Neither do I know the residue theorem or the estimation Lemma.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#23 2015-09-18 07:45:44
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Why isn't the Feynman Integration Trick Working?
M covers all of those things. It is nice to be able to understand it but when you can not you should still be able to compute and solve a problem. This is possible even when you do not grasp the concepts. See my signature, that was written by the great Von Neuman. If even he did not understand some math what chance do the rest of us have? Point is, I can not build an airplane, nor do I understand much about them but I can still fly in one. Understanding, like love comes later.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#24 2015-09-18 07:55:33
Re: Why isn't the Feynman Integration Trick Working?
It's OK -- I'll try to post a video or two summarising all of those concepts as best as I can. None of them are actually difficult to understand: in fact, using them, in this context, just comes down to algebra.
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