Integrating dx and dy: What Does It Mean?

  • Context: Undergrad 
  • Thread starter Thread starter Blue and green
  • Start date Start date
  • Tags Tags
    Dx Mean
Click For Summary

Discussion Overview

The discussion revolves around the interpretation of the differential elements dx and dy in the context of integration. Participants explore the meaning of these terms and their implications in mathematical expressions, particularly after integration has been performed.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • Some participants propose that dx and dy indicate the variable with respect to which integration has been performed.
  • Others argue that dx represents an infinitesimal unit of length along the x-axis, suggesting a geometric interpretation.
  • A participant challenges the notion that dx or dy should remain in the expression after integration, implying that they should be eliminated.
  • Another participant explains that dx can be viewed as a small piece of x, and integrating involves summing these small pieces, with the possibility of extending this idea to two dimensions with dx dy.

Areas of Agreement / Disagreement

There is no consensus on the role of dx and dy after integration, with some participants asserting they should be removed while others maintain they have ongoing significance. Multiple interpretations of these terms exist within the discussion.

Contextual Notes

Participants have not fully resolved the implications of retaining or discarding dx and dy post-integration, nor have they clarified the assumptions underlying their interpretations.

Blue and green
Messages
16
Reaction score
0
Once you've integrated, dx and dy just indicate what variable you've integrated in terms of, correct?
 
Physics news on Phys.org
Yeah. In response to the question in the title, dx does mean something.

One of the things that people associate with dx is an infinitesimal unit of length along the x axis.
 
"Once you've integrated"- that is after you have done the integration- there should no longer be a "dx" or "dy" in the expression!
 
As mentioned above dx just means "a little piece of x". So A dx is just the A times a little piece dx. Integrating means you do this many times, and add up the results. You can even do dx dy to have little squares, and other such things if you get clever!
 
  • Like
Likes   Reactions: davidbenari

Similar threads

High School What Is the Meaning of $\frac{d}{dx} \frac{dy}{dx}$?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Integration of ##e^{-x^2}## with respect to ##x##
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Landscape Fabric Roll
  • · Replies 8 ·
Replies
8
Views
3K
High School Orientation of double integrals
  • · Replies 13 ·
Replies
13
Views
2K
High School Where Did My Neglect of High-Order Terms Go Wrong in Integral Sums?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Integration with different infinitesimal intervals
  • · Replies 31 ·
2
Replies
31
Views
4K
Undergrad The Euler-Lagrange equation and the Beltrami identity
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Non solvable integral? (dx/dt)^2 dt
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad What is the meaning of dx and how does it relate to dy/dx?
  • · Replies 11 ·
Replies
11
Views
6K