Talk:Volume integral

Please, help to finish this page. Miraceti 00:55, 6 Dec 2004 (UTC)

Typo in TeX
Does anybody know how to write a nicer volume integral in TeX? Something like .Miraceti 00:55, 6 Dec 2004 (UTC)

Definition?
I thought volume integral meant an integral with respect to volume. Michael Hardy 22:37, 17 Mar 2005 (UTC)

Me too. But, the article has a link to Mathworld, where they define it as it was in the version you reverted. I would be inclined to think the Mathworld article is wrong. Oleg Alexandrov 22:56, 17 Mar 2005 (UTC)

V represents the closed region which the--Maciel 12:17, 26 Apr 2005 (UTC) volume would be calculated, F(x,y,z) doesn't represent a volume. F(x,y,z) maps the region V in R^3 into R^4. If f(x,y,z) = 1, then the integral is volume of V. take single variable integral Integral(f(x)) on interval [a,b] for example, [a,b] is a region in R^1, f(x) maps the region [a,b] into R^2, the integral represents the area under f(x) in R^2. If you set f(x) = 1, then you get b-a, it's the magnitude of [a,b].


 * Dear 142.150.160.186. Would you please make yourself an account? You can't always pop in and out using different IP address if you want to do something useful in here. If you make an account, you will have your own talk page, your stable watchlist, and life will be so much easier for you and for us, people who interact with you. Thanks. Oleg Alexandrov 17:08, 18 Mar 2005 (UTC)

Cleaning
The explanation of the different uses of the term "volume integral" is rather poor, being the two supposedly different examples equivalent. Both represent the integral of a function in a certain domain. While in the first example the function is a constant scalar function, in the second example we are dealing with a more generalized representation. Still, both represent the same concept without any differences between them.

The reference to the divergence theorem is redundant, regarding wikipedia as a whole. A simple reference to the wikipedia's article on that subject is not only more than enough, it also gives the reader a more indepth look at the subject. --Maciel 12:17, 26 Apr 2005 (UTC)


 * Agree with lots of the things you said. We had Chubby (see the history) who was adding all this stuff. However, I would like to say that you cut a bit too much. Can I challenge you to put some stuff back which would indeed illustrate what this article is about? A dry definition does not really do the job well. Oleg Alexandrov 17:51, 26 Apr 2005 (UTC)

triple integral of f(x,y,z) does not give volume, unless you generalize volume to R^n
The above is what an anon stated.

You see, you still believe volume integral is the integral of 1. Then, of course, the triple integral of a function f(x, y, z) is nothing but the integral in the region under the graph of w=f(x, y, z) in R4.

However, in the liteture, one sometimes uses volume integral synonimously with triple integral. This has to be reflected in the article.

Please write here any comments. Reverting back and forth is not the way to go. Oleg Alexandrov 16:24, 8 May 2005 (UTC)


 * No serious literature would mix volume integral with triple integral. (written, but usigned, by Chubby)

You are going to have a hard time proving that. :) Oleg Alexandrov 03:58, 5 Jun 2005 (UTC)


 * Also, please sign your comments, use four tildas, like this ~ . Oleg Alexandrov 03:58, 5 Jun 2005 (UTC)

Volume Element
Hello. Gooba has removed the "Volume integral in different coordinates" section (see history), which is fair enough as it probably doesn't belong here (in fact, I should really have asked here first ;-). However, I feel that this information should be provided somewhere in wikipedia, as that's what I wanted to know when I first searched for this page. I also searched in a few other places, like volume element and the coordiate systems page, but none have this information. If it is already provided, then can someone say where or put a link in somewhere. Sorry if that sounds like i'm having a rant, it's not supposed to be :-) h2g2bob H2g2bob 17:13, 26 Jun 2005 (UTC)


 * How about making a volume integral in different coordinates article,and linking to it from here and other places? Oleg Alexandrov 21:01, 26 Jun 2005 (UTC)

Parametric Form
What is so "suspicious" about the following:


 * $$\int\limits_D g\,dV = \iiint\limits_D g(\mathbf{x}(s,t,u)) \,{\partial \mathbf{x} \over \partial s} \cdot \left ( {\partial \mathbf{x} \over \partial t} \times {\partial \mathbf{x} \over \partial u} \right ) \,ds\,dt\,du.$$

where also
 * $${\partial \mathbf{x} \over \partial s} \cdot \left ( {\partial \mathbf{x} \over \partial t} \times {\partial \mathbf{x} \over \partial u} \right ) = {\partial (x, y, z) \over \partial (s, t, u)}.$$

It is true. Perhaps it should be reworded. Who has an idea of what how it should be better presented?

-- Lindberg 06:59, 2 December 2006 (UTC)

I think there should be a reminder that the scalar product of three vectors is fully antisymmetric. (See, for example, http://mathworld.wolfram.com/ScalarTripleProduct.html). Also, a reference to Jacobian matrix and determinant couldn't hurt. 198.228.228.169 (talk) 09:38, 15 June 2014 (UTC)Collin237

These examples are awful
We really should have at least one example that's not totally trivial, if we're going to have examples at all. 31.205.104.128 (talk) 23:30, 17 May 2017 (UTC)