Integration Volume: Disc vs Shell - What's the Difference?

Click For Summary

Homework Help Overview

The discussion revolves around understanding the differences between disk and shell integration methods for calculating volumes of solids of revolution. Participants are exploring the contexts in which each method is applicable and seeking clarification on the underlying concepts and formulas.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster seeks to understand the differences between disk and shell integration, including their respective applications. Some participants provide insights on the axis of rotation and the geometric interpretations of each method. Questions about the general vector equation of a solid of revolution are also raised.

Discussion Status

The discussion is ongoing, with some participants offering explanations about the methods and their applications. The original poster expresses a desire to further investigate the topic and indicates that the responses have helped clarify some confusion.

Contextual Notes

There is an indication that the original poster is looking for more detailed explanations and may have constraints related to their understanding of the formulas involved in shell integration.

pavadrin
Messages
154
Reaction score
0
there are the two types of volume integration which i am aware of, disc-integration and shell integration. What is the difference between these? where would each one? Also i was looking at shell integration on carious sites on the net, and i am still a little confused how the generic formula works. Could someone ever so kindly explain this to me?

many thanks,
pavadrin
 
Physics news on Phys.org
The difference between disk and shell integration is where the axis of rotation is. Let's assume that you are integrating a solid of rotation of some f(x)dx. If the axis of rotation is parallel to the x-axis then you use disk integration, but if the axis of rotation is perpendicular to the x-axis then you use shell integration.
 
How would you find the general vector equation of a solid of revolution?
 
"Disks" works, of course, by using disks- normally, the radius of the disk is the value of the function and you calculate the area by [itex]\pi f(x)[/itex], multiply by the "thickness", dx, and then integrate.

"Shells" works by using thin cylinders. The radius is typically the x-value so you have a "circumference" calculation [itex]2\pi x[/itex] and then multiply by the "height" of the cylinder, f(x): you integrate [itex]2\pi x f(x) dx[/itex\.[/itex]
 
okay thanks for the replies
it is a little less confusing now
ill try reading into in more and repost if i am still stuck,
thanks once again for your time,
pavadrin
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
Replies
4
Views
2K
Replies
17
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
9
Views
2K
Replies
2
Views
2K
  • · Replies 8 ·
Replies
8
Views
5K
Replies
4
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K