Why is the volume integral of zero equal to zero?

Click For Summary

Discussion Overview

The discussion revolves around the concept of volume integrals, specifically addressing why the volume integral of zero results in zero. Participants explore the differences between types of integration, including indefinite and definite integration, and the implications of treating zero as a constant in these contexts.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant questions why the volume integral of zero is zero, suggesting a connection to the idea that the integral of zero is a constant.
  • Another participant clarifies that there are different types of integration involved, distinguishing between volume integrals and indefinite integrals.
  • A third participant elaborates on the volume integral of zero, stating that since zero is a constant, it can be factored out, leading to the conclusion that the integral evaluates to zero.

Areas of Agreement / Disagreement

Participants appear to have differing views on the interpretation of integration types and their implications, indicating that the discussion remains unresolved regarding the conceptual understanding of volume integrals versus indefinite integrals.

Contextual Notes

There are limitations in the discussion regarding the definitions of integration types and the assumptions made about constants in integrals, which have not been fully explored or resolved.

tomwilliam2
Messages
117
Reaction score
2
If the integral of zero is a constant, then why is the volume integral of zero just zero?
 
Physics news on Phys.org
You're addressing two types of integration. <Volume integrals> can be expressed as interated definite integration, while <integral of 0 is a constant> means that you're speaking of indefinite integration.
 
tomwilliam2 said:
If the integral of zero is a constant, then why is the volume integral of zero just zero?

Consider the expression ##\displaystyle \iiint\limits_{V}0 \, dV##, which I believe you mean by "volume integral". Since 0 is, itself, a constant, we can pull it out front, getting ##\displaystyle 0\iiint\limits_{V} \, dV = 0V = 0##
 
Thanks, both of you.
 

Similar threads

Undergrad Why Does an Integrand Equaling Zero at x=1 Not Determine the Integral's Value?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Double integrals - do areas cancel?
  • · Replies 24 ·
Replies
24
Views
4K
High School Question about volume of a sphere
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Calculating the change of the volume of a sphere using this integral
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Relating integration of forms to Riemann integration
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
4K
High School Modelling object w/ functions, how to find volume loss from indents?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Equivalence of alternative definitions of conservative vector fields and line integrals in different metric spaces
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Why is this closed line integral zero?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Volume of revolution -- Why use this integral?
  • · Replies 13 ·
Replies
13
Views
2K