From Wikipedia, the free encyclopedia
Jump to: navigation, search
Former good article nominee Integral was a good articles nominee, but did not meet the good article criteria at the time. There are suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
October 23, 2006 Good article nominee Not listed
edit·history·watch·refresh Stock post message.svg To-do list for Integral:

Here are some tasks awaiting attention:
  • Article requests : * the article seems to lack focus and order, and there is no table of contents. Also, brief discussions on the general properties of the integral such as being a linear functional, along with two brief sections on the two definitions of the integral.
    • treatment of integrals with regard to differential forms.
    • Some images to illustrate the Informal discussion section. Like what?--Cronholm144 21:49, 28 June 2007 (UTC)
    • A (sub)section on "Properties of integrals" covering general properties as a linear functional, Fundamental theorem of Calculus, etc.
    • Copyedit : * Once major changes are complete, a thorough copyedit for flow and consistency is in order.
    • Expand : * the section on Computing integrals could do with some expansion.

WikiProject Mathematics (Rated B-class, Top-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
B Class
Top Importance
 Field: Analysis
One of the 500 most frequently viewed mathematics articles.
This article has comments.
Wikipedia Version 1.0 Editorial Team / v0.7
WikiProject icon This article has been reviewed by the Version 1.0 Editorial Team.
Taskforce icon
This article has been selected for Version 0.7 and subsequent release versions of Wikipedia.
B-Class article B  This article has been rated as B-Class on the quality scale.

Transport function[edit]

I'm not totally sure, as the article on the "transport function" is very short, but I'm pretty sure that the "transport function" is NOT a definition of the integral as is stated in this article on integrals. (talk) 01:23, 11 April 2012 (UTC)


At the moment this article tries to cover too much. It might be in order to split it into an article on single-variable, real-valued integration (which could then talk much more about applications of these basic integrals), and a more general article on integration, its history, and a list of types of integration written in summary style. — This, that, and the other (talk) 09:45, 13 May 2012 (UTC)

I think the length and coverage are about right for a top level article like this. There's already summary style happening in each section. I don't find the emphasis on any one topic to be overwhelming. Overall, it's a well-balanced article of an appropriate length. The main deficiency is better citation style. Sławomir Biały (talk) 12:06, 13 May 2012 (UTC)

Everywhere continuous but nowhere differentiable functions[edit]


According to my sacred texts, any continuous function on the closed interval [a,b] is Riemann integrable over that interval. Now there exist functions satisfying that condition - hence integrable - but nowhere differentiable. So, forgive me my ignorance, but I take this to mean that the integrated function (although it can't be expressed in a closed form) is differentiable, once. It seems a bit screwy. Have I misunderstood something? In any case, might it be worth mentioning integration and these functions in the article regarding Riemann integration? All the best (talk) 16:13, 28 July 2013 (UTC)

Whoops! My mistake. I was talking about a definite integral which has, of course, a numerical result. I beg yoyr forgiveness, but I still think that nowhere continuous functions deserve a mentions. All the best. (talk) 17:12, 28 July 2013 (UTC)
You might appreciate differentiability class. Ozob (talk) 20:17, 28 July 2013 (UTC)

Recent edit[edit]

I am writing here about this edit, whose edit summary reads "Layout/formatting changes and formatting/cleanup templates added. Moved history section to the end of the body and moved an oversized image out of the lead. This page really needs a lead rewrite." My inclination is to revert this edit, since I disagree with everything that it did:

  1. The edit removed the image from the lead, with no real justification except to say that it was oversized. It is not an oversized image: in fact its dimensions are quite typical for a lead image.
  2. The edit added the template {{lead rewrite}} with the justification "The current lead section lacks sufficient generality to summarize all forms of integrals (and hence, the article)". It may well be true that the current lead does not summarize all forms of integration, however it does support the article as currently written. All aspects of the article are summarized in the lead, roughly in proportion to their prominence in the article.
  3. The edit added the template {{too many photos}}. I can't see how this is remotely the case. Many sections have a single image in support, the chief exceptions being the section on Riemann integration which has two, and the long introduction section which has three (that comfortably fit within that section). This does not seem at all to be excessive.
  4. Moving the history section to the very end of the article seems to run against the purposes of WP:MTAA. The history is the most accessible portion of the article, so it should be nearer to the top than to the bottom.

--Sławomir Biały (talk) 11:40, 21 October 2013 (UTC)

  • That's not everything I did in my edit - you reverted changes that addressed conformity problems with WP:IMAGELOCATION and WP:LAYIM - (see formal definitions section where the line is cut). MOS indicates there are too many images when there's overrun into another section. I put in a temporary fix with the "clear" template, which you then reverted. The ideal fix would be to use a gallery to group the images neatly, not delete images.
  • The sandwiched text between the left and right images under Riemann integral is (IMO) the worst MOS flaw/appearance issue on this page. (WP:IMAGELOCATION) If you don't like my fix, you need to do something else to address it.
  • The TOC is extending the lead section due to its excessive size and position - the only solution I know of for fixing that is a TOC limit.
  • Neither the first definition, nor the first paragraph of the lead, sufficiently define the integral conceptually or mathematically in a general context (which would describe the integral of a map over an arbitrary space). At minimum, it should mention more general integrals (i.e. types of integrals and spaces over which one can integrate) in this paragraph. I do not think it's a good idea to use a mathematical definition of the integral in this general context, because that would be too technical for most readers; however, I think it's absolutely necessary (it's also indicated in WP:LEAD and more specifically in WP:GOODDEF) to adequately describe integration in general terms, not in specific cases. The current lead would be great for an article on Riemann integration on the real line; but, you'll need to explain to me exactly how the first paragraph reflects upon a Lebesgue integral over an arbitrary/general measure space, because I don't see it. I can't think of an adequately general definition/description off the top of my head, but it should answer the question, "What does the integral of a mapping actually represent in practical terms?"
  • I think you raised a good point about keeping the history section as the first section though.
  • Also, I misread the source code information on my browser when I checked the lead image - I read the default size (420px) instead of the current size (300px) For future reference, a lead image is "oversized" (by policy definition) if it is >300px, per WP:LAYIM. So that was a reasonable thing to revert.
How would you prefer to address these remaining issues? Seppi333 (talk) 17:37, 21 October 2013 (UTC)

I missed some minor formatting changes, but the edit was not adequately summarized. (It would be more helpful to roll this out as a sequence of edits, each with an informative edit summary about precisely what was done rather than relying exclusively on a diff to determine what had changed.) I have fixed the text squashing issue and set the TOC limit to 2.

I don't really follow your point about the lead being too specific. The Lebesgue integral also measures the signed area under the graph of a function, so it's not overly specific to context of the Riemann integral. It would be inappropriate to attempt in the first paragraph to emphasize the general case of an abstract measure space since this is treated only briefly in the body of the article itself. Whether this focus is appropriate is ostensibly a problem with the article, not with the lead. Sławomir Biały (talk) 21:29, 21 October 2013 (UTC)

I'll put in a gallery and add content on the Lebesgue integral once I've finished taking amphetamine to FA status. For the lead, I really just meant the definition or description should encompass that kind of integral over that form of space in addition to a Riemann integral on R. Basically, what's stated doesn't describe the mathematical term "integration" in general - so it's incomplete, not wrong. I'll contact you for your input on addressing this when I'm ready to work on it (assume it isn't fixed before then).
Regards, Seppi333 (talk) 17:25, 22 October 2013 (UTC)
I'm not sure what content you had in mind with respect to the Lebesgue integral: the lead already mentions that way of integration and, moreover, already includes the basic intuition that is common to both Riemann and Lebesgue integration. For readers wishing to know more about these different notions of integration, there are actually separate articles Lebesgue integral and Riemann integral. However, there are many other kinds of integrals: for instance the Denjoy integral, the Henstock–Kurzweil integral, the Daniell integral, the Gelfand–Pettis integral, the Riemann–Stieltjes integral, the Lebesgue–Stieljes integral, and so forth. So it's not at all clear what your ideal lead should look like, nor how you could possibly reference such a lead that encompasses all of these standard generalizations of the usual integral (nor whether such an attempt would actually be an improvement for the typical reader of this article).
While I would enjoy immensely a serious attempt to clarify to another mathematician what the noun "integral" actually means, I should caution that there is ostensibly a plethora of different notions of "integral" that might be of interest to, say, a high school student, an undergraduate major in the sciences, a mathematics major, a graduate student, or a mathematics researcher. This article, as a top-level article on the topic, should probably cater to the least common denominator of this group. The most common intuition is the area under a graph, as the lead already discusses, and this intuition is actually valid for both the Riemann and Lebesgue integrals. A specialist interested in a particular kind of integral should be able to navigate easily to more specialized articles (there are links in the text as well as navboxes and categories) whereas a novice needs a description of the topic that is familiar and easy to understand.
The bottom line is that if you find that our treatment of the Lebesgue integral is lacking, then the appropriate article to edit is Lebesgue integral, not necessarily the main page Integral, just as if you were to feel that we did not adequately address the difference between the Henstock&endash;Kurzweil integral and the Daniell integral, for example, then the appropriate place for that discussion would be on some subordinate article. Sławomir Biały (talk) 00:45, 27 October 2013 (UTC)
Hi Slawomir, I'm still not ready to work on this yet, so I won't be able to really follow up - but the very least that I can say is that when I do work on it, I'd be using WP:RS as is required - my own definition is moot in relation to the topic. I'm well aware that there are many different types of integrals. That's precisely why such a definition in the lead should encompass integration theory in general. Regards, Seppi333 (talk) 01:33, 27 October 2013 (UTC)