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	Integral was a good articles nominee, but did not meet the good article criteria at the time. There may be 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.
Article milestones Date Process Result October 23, 2006 Good article nominee Not listed

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Mathematics Top‑priority 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.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles Top This article has been rated as Top-priority on the project's priority scale.

To-do list for Integral: edit · history · watch · refresh · Updated 2007-11-09 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.

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[1] breaks out separate sections for analytical vs symbolic integration, but I was raised that analytical and symbolic mean the same thing in this context. Is there some different meaning I'm not aware of? Rolf H Nelson (talk) 04:56, 4 January 2022 (UTC)[reply]

I agree. It's not clear what the distinction is supposed to be. In fact, there is a great deal of overlap in the content, as it is currently written. Unless somebody chimes in with a strong explanation, I'd support merging the two sections. Mgnbar (talk) 13:40, 4 January 2022 (UTC)[reply]

I also agree that the article is muddled: finding an antiderivative is described in both the "Analytical" and "Symbolic" subsections. The article can be improved.

• The main division is usually between those methods that find a formula containing well-known functions, and those methods that directly find a numerical value. I have seen the latter methods referred to as "approximate integration". But Wikipedia already has articles on symbolic integration and numerical integration so they are probably the best terms to use.

• I have seen methods of solving differential equations classified as "graphical", "numerical" or "analytical". But I am not sure how much the term analytical integration is used. There could be a distinction between methods that use clever mathematical analysis thinking and those that use brute-force calculation. Or perhaps analytical integration only applies to analytic functions. The term symbolic integration is probably becoming more popular because it is used in computer algebra systems.

• The current "Analytical" and "Symbolic" subsections both mention methods that find a symbolic representation as an infinite series which is then evaluated numerically. I have seen such methods classified as "approximate", and they could go in the "Numerical" subsection. But it might be better to have them in a separate subsection under the traditional name "Integration by series".

• I do not agree with the "Analytical" subsection where it says that "The most basic technique for computing definite integrals of one real variable is based on the fundamental theorem of calculus". A numerical method such as counting squares under a graph is much simpler to explain.

• Also, I would change the name of the "Mechanical" subsection to "Analogue" and include links to both differential analyser and electronic analogue computer. JonH (talk) 16:43, 16 May 2022 (UTC)[reply]

Rubi, a computer algebra system rule-based integrator, pattern matches an extensive system of symbolic integration rules to integrate a wide variety of integrands.^[1]

The bracket integration method is a generalization of Ramanujan's master theorem that can be applied to a wide range of integrals.^[2]

• Gonzalez, Ivan; Jiu, Lin; Moll, Victor H. (1 January 2020), "An extension of the method of brackets. Part 2", Open Mathematics, 18 (1): 983–995, doi:10.1515/math-2020-0062, ISSN 2391-5455

• Rich, Albert; Scheibe, Patrick; Abbasi, Nasser (16 December 2018), "Rule-based integration: An extensive system of symbolic integration rules", Journal of Open Source Software, 3 (32): 1073, doi:10.21105/joss.01073

TMM53 (talk) 08:23, 2 January 2023 (UTC) TMM53 (talk) 08:23, 2 January 2023 (UTC)[reply]

I added this content and 2 references.TMM53 (talk) 03:12, 23 March 2023 (UTC)[reply]

I am trying to improve the lead sentence since it came up in the village pump as an example of something that needs work. My contribution is based on the suggestions from a WikiProject:Mathematics discussion Thenub314 (talk) 16:19, 10 February 2023 (UTC)[reply]

Is there a reason this article doesn’t include the standard definition for the Riemann integral? i.e.

$${\displaystyle \int _{a}^{b}f(x)dx=\lim _{n\to \infty }\sum _{i=1}^{n}f(x_{i})\Delta x}$$

In your definition, what is ${\displaystyle x_{i))$? There are several conventions for how it could relate to a, b, and n. This article presents one of these conventions, in the "Formal definition" section. I'm not an expert on the history, but I think that it's based on Riemann's original formulation. A different convention leads to the upper and lower Darboux integrals, which are a bit simpler.

So I think that you're asking why the article presents Riemann integrals instead of Darboux integrals. That's a fair question. I don't know the answer. Mgnbar (talk) 01:05, 8 November 2023 (UTC)[reply]

The redirect Integration with other techniques has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 January 31 § Integration with other techniques until a consensus is reached. Steel1943 (talk) 21:04, 31 January 2024 (UTC)[reply]