# Talk:Disc integration

WikiProject Mathematics (Rated Start-class, Low-importance)
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:
 Start Class
 Low Importance
Field:  Analysis

Do we need to standardize "disc" vs. "disk?"

I can't think of anything I missed when I wrote this, perhaps it needs to be rewritten for the non-math major. But I have to admit that I'm sort of offended that it is "tagged for cleanup". I spent well over an hour writing a page for the disc method trying to be as clear and thorough as possible. Would someone just leave some feedback as to what is wrong with it instead of just saying "It's wrong??!!"

Um, to the above point, its not "wrong", just formatted improperly. Space it out, add some sections in there, etc (I think thats what is wanted).

what textbook did this come out of? Kingturtle 22:33, 28 Sep 2003 (UTC)

This didnt'. LirQ

• I am just curious where this info came from. Do you have all those formulas memorized? Kingturtle 00:22, 29 Sep 2003 (UTC)

i have an exam on this today. 128.211.218.138 19:55, 5 February 2007 (UTC)

Is this right?

• Horizontal Axis of Revolution
• V = π ∫ [R(x)]2 dy

Surely that should be dx, not dy? Fredrik 07:27, 30 Apr 2004 (UTC)

In calculus, the disc method is one of two popular methods (other is the "shell method") used in order to calculate the volume of a shape obatined by revolving the locus of a two dimensional equation around a straight axis (called the "axis of revolution"). Most commonly the axis of rotation is horizontal or vertical. This method models the generated 3 dimensional shape as a "stack" of an infinite number of cylinders (of varying radius) which are infinitely thin. One can think of it as stacking different sizes of coins on top of each other. This "stack" is called a "solid of revolution".
If the function to be revolved is a function of x, the following integral will obtain the volume of the solid of revolution: ${\displaystyle \pi \int _{a}^{b}[R(x)]^{2}dx}$ where R(x) is the distance between the function and the axis of rotation. This works only if the axis of rotation is horizontal (example: y = 3 or some other constant).
If the function to be revolved is a function of y, the following integral will obtain the volume of the solid of revolution: ${\displaystyle \pi \int _{a}^{b}[R(y)]^{2}dy}$ where R(y) is the distance between the function and the axis of rotation. This works only if the axis of rotation is vertical (example: x = 4 or some other constant).
To obtain a "hollow" solid of revolution, the procedure would be to take the volume of the outer solid of revolution and subtract from it the volume of the inner solid of revolution. This can be calculated in a sigle intgral simular to the one following: ${\displaystyle \pi \int _{a}^{b}[R_{O}(x)]^{2}-[R_{I}(x)]^{2}dx}$ Where RO(x) is the function that is farthest from the axis of rotation and RI(x) is the function that is closest to the axis of rotation. One should take caution not to evaluate the square of the difference of the two functions, but to evaluate the difference of the squares of the two functions. ${\displaystyle [R_{O}(x)]^{2}-[R_{I}(x)]^{2}\not \equiv \;[R_{O}(x)-R_{I}(x)]^{2}}$

## The calculus sidebar

I think, since this article is in the Category:Calculus, people could just click on that category and find calculus related articles, rather than keep a calculus sidebar of links on every page. Wonder what other people think. Oleg Alexandrov 15:36, 3 May 2005 (UTC)

I'm also starting to dislike those sidebars, but perhaps it would be best to first convert it to a footer. --MarSch 14:35, 28 October 2005 (UTC)

In Reply to Fredrik: For the disc method, the representative rectangle will be perpendicular "long wise" to the axis of rotation. For the shell method it will be parallel to the axis of rotation.

## Reversion of page move

This page was recently moved from Disk integration to Disc integration, with the editor's justification being "This is the spelling used in the intro". However, the page was created using American English, and it remained in that form until this revision, when an anonymous IP rewrote the article and converted to British English in November 2005. Bizarrely, the IP in question, 128.123.202.11, resolves to New Mexico State University.

As specificed in an ArbCom ruling of June 2005, it is inappropriate to change from one style to another, and editors should defer to the style used by the first major contributor. I'm therefore changing all instances of "disc" to "disk", and restoring the original page. Please note that I am American neither by birth nor residence, so this is not nationalism run riot, merely proper application of WP rules. --DeLarge 20:10, 5 March 2007 (UTC)

No problem - as long as the article is internally consistent, I am happy! I moved it from Disk integration to Disc integration for consistency, but also for the simple reason there was no redirect from Disc integration at the time, and this was a fast way to do it! It was a good faith edit indeed, but not an error. Although I do not really care whether this article is spelt with a c or a k, I disagree with your reasoning: "disk" vs "disc" is more complicated nowadays than American vs. British English (see Disc or disk (spelling)) and the ruling you cite talks mainly about the stability of an article and only refering to the original contributor "if in doubt". My impression is that mathematicians, even American ones, tend to refer to disc's with a 'c', perhaps because we use a lot of greek, or maybe because we tend to view things optically rather than magnetically :) So don't be surprised by the New Mexico State University IP address: I bet the editor was a mathematician. Geometry guy 00:35, 14 March 2007 (UTC)

## Kudos

I have an exam on this in a few days, and found that the equations and formulae were very helpful. I just wanted to give my props to everyone who wrote this article - thank you very much! 68.149.170.235 (talk) 02:44, 16 December 2012 (UTC)Fahim from Alberta 19:44, 15 December 2012 (GMT)