Talk:Integration by substitution
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[edit] conditions on f
In most calculus books f is required to be continuous (not just integratable), mainly because
their proofs are based on the fundamental theorem of calculus which requires continuity.
See also:
http://eom.springer.de/I/i051740.htm
http://mathworld.wolfram.com/ChangeofVariablesTheorem.html
However i've seen abstract generalization (based on lesbegue integrals) that seems to skip the contintuity condition for f (i do not fully understand the terms involved):
http://planetmath.org/encyclopedia/ChangeOfVariablesFormula.html
It would be nice if somebody knowledgeable could confirm/comment this and modify the article (there should be at least a note why or under which exact condition continuity can be dropped for f).
[edit] which phi?
I replaced φ with Φ, since the latex \phi looks like that one. This may however differ depending on which font you are using...
I don't think thats strictly right. Φ is capital phi, φ is not italicized phi, and φ is italicized phi, which I think is the strictly correct one. I'll leave it up to you to revert if you think it should be done. PAR 20:13, 22 Mar 2005 (UTC)
φ and φ are alternate lowercase forms of phi (uppercase Φ). Both are accessible through LaTeX, via \varphi and \phi, respectively. —Caesura(t) 15:19, 16 October 2005 (UTC)
Fine article. To those responsible: thanks. --Christofurio 17:20, Apr 23, 2005 (UTC)
I agree with Karesser on this. For most people who will be using the article phi just adds confusion. Is there any reason why it should be phi, because all the calculus books I have seen use g(x). Bizzako 21:54, 16 December 2006 (UTC)
[edit] Requested move
speedy move according to WP standards for upper/lower case in article names. --Trovatore 02:44, 7 December 2005 (UTC)
[edit] Voting
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[edit] Discussion
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[edit] Move issues
I moved this article back from Integration by Substitution. The reasons are three:
- The page was moved against Wikipedia conventions for capitals; it should have been integration by substitution
- The double redirects were not fixed.
- I don't quite see any discussion about why the move would be necessary.
So, if it is decided to move this page indeed to integration by substitution, I can help (you would need an administrator to delete the redirect at integration by substitution first). But I would like to see if people agree on that, and somebody's got to promise to fix the redirects afterwards. Oleg Alexandrov (talk) 03:45, 7 December 2005 (UTC)
- Maybe I rushed things a bit with the "requested move" process. I don't have any strong preference for Integration by substitution over Substitution rule; I just tried to move Integration by Substitution to Integration by substitution to comply with the capitalization convention, and then nominated the article when I found out I couldn't just move it. I suppose I think Integration by substitution is just epsilon better than Substitution rule, but I'd be happy to have the nomination quashed and things left as they are now if that's simpler. --Trovatore 04:08, 7 December 2005 (UTC)
- Let us see what Atraxani says, the user who did the move (I wrote that user a message). All that really matters is that whoever wants to do the move should fix the redirects, to avoid redirects to redirects. Oleg Alexandrov (talk) 04:13, 7 December 2005 (UTC)
- OK, I did the move and fixed the redirects myself. I guess that's the best thing to do. A message to Atraxani though, please do use more care when moving pages. Oleg Alexandrov (talk) 18:11, 9 December 2005 (UTC)
- Let us see what Atraxani says, the user who did the move (I wrote that user a message). All that really matters is that whoever wants to do the move should fix the redirects, to avoid redirects to redirects. Oleg Alexandrov (talk) 04:13, 7 December 2005 (UTC)
[edit] Multi value thing
If one is required to substitute the variable x in the original integral to something like u^2-u-2, what do you do with the limits? There are obivously two solution of u for each x, so how can one tell which one to use?
[edit] integrability of phi
Is it necessary to suppose integrability of (phi)'? Isn't it guaranteed by its assumption of continuity?
[edit] The Calculus Tempate For This Page
It seems that this is the only page that uses the Calculus Template whose link does not become bold and unlinkable when on the page. I don't know how to fix this. Ryulong 20:25, 6 February 2006 (UTC)
- That is because the link in the Calculus template used to point to substitution rule. I changed it to point directly to this page, integration by substitution, and now the link does become bold. -- Jitse Niesen (talk) 22:06, 6 February 2006 (UTC)
[edit] Expansion of Substitution rule for multiple variables
It would be great if someone expanded the Substitution rule for multiple variables section with examples and further explanations. Thanks, --Abdull 14:20, 25 May 2006 (UTC)
- Yes. Here is something that is rather subtle but bothers people as I know from experience. When the number of dimensions is 1, the multi-variable formula should match the one-variable formula. However, the multi-variable formula has that absolute value in there. In the one-variable formula we have φ'(t) not |φ'(t)|. Explaining why this is not actually a contradiction is an expository challenge. McKay 02:10, 6 March 2007 (UTC)
