Talk:Integral

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This article is devoid of sources. Sad.

Much of it seems like an essay which is not good encyclopedic practice at least with the high standards of english wikipedia. — Preceding unsigned comment added by Yoandri Dominguez Garcia (talk • contribs) 14:50, 15 June 2018 (UTC)

Currently the article has more than 20 titles in a bibliography and more than 10 links to on-line texts. Furthermore, the template for integrals at the end of the article links to many types of integral where specialized sources can be found. As an article about a common college topic found in textbooks, in-line references are not appropriate. — Rgdboer (talk) 01:37, 30 October 2019 (UTC)

@Rgdboer: You say "in-line references are not appropriate". Are you quoting the Wikipedia Manual of Style or Mathematics guidelines? I have looked in those documents and found nothing about in-line references being inappropriate in articles on the topic of mathematics, or less valuable than articles on other topics.

Over the years, nine Math articles have been raised to Featured Article status. Those nine, and their number of in-line citations are as follows:

• Pi 223 in-line Citations

• Euclidean algorithm 158 in-line Citations

• Logarithm 109 in-line Citations

• Group (mathematics) 79 in-line Citations

• Parity of zero 75 in-line Citations

• 0.999… 71 in-line Notes and Citations

• Problem of Apollonius 66 in-line Citations

• Polar coordinate system 22 in-line Citations

• 1-2+3-4+… 21 in-line Notes and Citations

There may be some truth in the idea that articles about Mathematics do not require as many in-line citations as articles on other topics. If that is so, the Mathematics guidelines should be amended to make it clear and put the matter beyond dispute. Until then, I think User:Yoandri Dominguez Garcia is justified in drawing our attention to the fact that this article does not meet Wikipedia’s standards regarding in-line citations. Dolphin (t) 11:18, 30 October 2019 (UTC)

Hyperbola quadrature

@Deacon Vorbis: The reversion of my contribution concerning hyperbola quadrature and its place in the History of Integration suppresses useful information. "Unreferenced" says the edit summary, yet Introduction to the Analysis of the Infinite is part of the contribution. Although it is an Original Source there is an article on that book from 1748, and our article has several secondary sources, including Henk Bos who concurs with what was contributed here. Also, referring to History of logarithms there is a statement by D. T. Whiteside that supports the contribution. This material is very old so accusations of OR such as you raised July 18 this year in Talk:Natural logarithm are bogus. The time you put in to improve this Project is appreciated; however, it appears you are repressing information about the century (1647 to 1748), before natural logarithm, when hyperbola-quadrature was used. Why not tag the contribution with "citation needed" rather than revert. Restoration of the contribution is requested by this Talk, perhaps citing Whiteside. Please respond since dialogue here is required before appeal to a higher venue. — Rgdboer (talk) 20:39, 30 October 2019 (UTC)

@Rgdboer: Please see WP:BURDEN. You added quite a lot of information without providing any sources. Providing your own analysis of primary sources (if that's what you did; I can't tell) is most definitely OR. Less importantly, the material added wasn't well-formatted (e.g. there were a lot of minor grammar problems, none of the math was placed inside {{math}}/{{mvar}}, and some wasn't even italicized), but that can be fixed. There were also some problems with the style of the prose; that's more difficult to fix without having a source to refer to – another important reason to include them. For just one example, you said, "Promulgation of the hyperbola-quadrature by Huygens and Nicholas Mercator assured the transcendental function's acceptance." This is kind of confusing, and I, for one, wouldn't be able to clear it up without having a source to refer to. A claim such as this really needs a source anyway. –Deacon Vorbis (carbon • videos) 21:02, 30 October 2019 (UTC)

Signed Area redirect?

I don't believe that "Signed Area" should redirect to this "Integral" page. When I hear "signed area" I don't think only of the "areas are negative below the x-axis" convention for integrals. I also think of the related-but-more-general concept of, say, considering areas of regions enclosed by counter-clockwise paths as positive and clockwise paths as negative. This comes up very naturally when considering, say, the Shoelace formula. --Helopticor (talk) 13:05, 19 April 2020 (UTC)

Formal definition of the Riemann integral

This is a small point. I spotted a mistake in the definition of the Riemann integral, which included the following segment:

For all $\varepsilon >0$ there exists $\Delta _{i}>0$ such that, for any tagged partition $[a,b]$ with mesh less than $\Delta _{i}$,

$\left|S-\sum _{i=1}^{n}f(t_{i})\,\Delta _{i}\right|<\varepsilon .$

This is a typical argument of the epsilon-delta type. The mesh of a partition is the width of the largest sub-interval formed by the partition. If the width of the largest sub-interval (with some index k which we don't need to know) is $<\delta$, this implies that for all subintervals $\Delta _{i}$ are $<\delta$. No need to go at the level of indices or of taking into account the plurality in the notation: the notion of mesh does the job.

So the correct formulation should be (and using lower case delta makes the argument even clearer, showing that it is the familiar epsilon-delta argument:

For all $\varepsilon >0$ there exists $\delta >0$ such that, for any tagged partition $[a,b]$ with mesh less than $\delta$,

$\left|S-\sum _{i=1}^{n}f(t_{i})\,\Delta _{i}\right|<\varepsilon .$

I will try again, asking all those who want to revert my change to read the above comment and indicate where it goes wrong, if you find something wrong with it.

Dessources (talk) 13:13, 15 August 2021 (UTC)