Talk:Calculus/Integration/Archive 1

Are you sure it's a good idea to write this chapter before the previous ones? As it is, we will have to (and already are) making assumptions about what will be taught in them. IMO we should write the chapters in order. Anybody have comments? Eric119 17:24 26 Jul 2003 (UTC)


 * Well, when I have time, I'll go fill in the others. The stuff on differentiation requires nice pictures and demonstrative examples, which will take a lot of time to fix and prepare, whilst integration is more a symbolic thing and most of it can be written without having diagrams and such (but they will be needed later)
 * Hope this clarifies things... Dysprosia 00:37 2 Aug 2003 (UTC)

Is it just me or are some of the  $$...$$  tags producing text instead of images? --Matt 03:55, 12 Jun 2004 (UTC)
 * Nevermind my question... --Matt 07:40, 12 Jun 2004 (UTC)

Fundamental Theorem of Calculus
Perhaps I missed it (completely possible as I'm a bit of a Wiki newbie) but I didn't see mention of the Fundamental Theorem of Calculus (FTC). IMHO, the FTC is one of the most "surprising results" in mathematics. First, I think that integration is not really about finding anti-derivatives, though certainly it involves using them. Integration is about infinite sums (of areas). Second, the surprising thing is that if we look at a function (f) between A and B, find the anti-derivitive of f (F), then take Fs value at B and subtract Fs value at A then that gives us (drum roll please) the exact area under the curve (f) between A and B! How??? Of course, there is a good reason but the FTC was, and I think still is, a rather surprising thing to discover.

Okay, this is starting to look like a rant... sorry. Wistful recolleciton of my days teaching college Calculus, I suppose. Anyway, please let me know if I simply missed it somewhere -- maybe it's planned but not written or something like that. Thanks.

Exception
It should be explicitly noted, although it is implied by the (alpha + 1) factor in the denominator, that the power rule for integration does not hold for alpha = -1.


 * Of course. Dysprosia 04:56, 3 Feb 2005 (UTC)