Why is the volume integral of zero equal to zero?

Click For Summary
The discussion clarifies that the volume integral of zero equals zero due to the nature of integration types. Volume integrals are treated as iterated definite integrals, while the integral of zero refers to indefinite integration. The expression for the volume integral of zero, represented as ∭V 0 dV, simplifies to zero because zero is a constant that can be factored out. Thus, the result of the volume integral remains zero regardless of the volume V. Understanding these distinctions in integration types is crucial for grasping why the volume integral of zero is zero.
tomwilliam2
Messages
117
Reaction score
2
If the integral of zero is a constant, then why is the volume integral of zero just zero?
 
Mathematics 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.
 

Thread 'Leibniz Rule Videos on Digital-University'

Good morning I have been refreshing my memory about Leibniz differentiation of integrals and found some useful videos from digital-university.org on YouTube. Although the audio quality is poor and the speaker proceeds a bit slowly, the explanations and processes are clear. However, it seems that one video in the Leibniz rule series is missing. While the videos are still present on YouTube, the referring website no longer exists but is preserved on the internet archive...
View full post »

Similar threads

High School Modelling object w/ functions, how to find volume loss from indents?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Volume of revolution -- Why use this integral?
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad How to prove that a scalar potential exists if the curl of the vector point function is zero?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Higher Dimensional Spheres viz. Cubes
  • · Replies 1 ·
Replies
1
Views
1K
High School How to calculate a hollow cylinder's volume without the hollow center?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Measure of non-periodicity of almost periodic functions
  • · Replies 1 ·
Replies
1
Views
2K
High School Need some clarification to get dimensions for a volume
  • · Replies 5 ·
Replies
5
Views
2K
High School Gradient of scalar field is zero everywhere given boundary conditions
  • · Replies 3 ·
Replies
3
Views
2K
Insights Why Division by Zero is a Bad Idea
  • · Replies 47 ·
2
Replies
47
Views
6K
MHB Calculating Sand Volume for a Cylindrical Containment Vessel
  • · Replies 2 ·
Replies
2
Views
1K