Difference Between d3x and triple Integral

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Discussion Overview

The discussion revolves around the difference between the notations ∫d³x and ∫∫∫dxdydz, focusing on their usage in the context of triple integrals in mathematics. Participants explore the implications of these notations in theoretical and practical applications.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the difference between the notations ∫d³x and ∫∫∫dxdydz, expressing confusion.
  • Another participant suggests that there is no difference between the two notations.
  • A third participant points out that the notation ∫d³x is less common and mentions that the more usual form for a triple integral is ∫₍D₎ dV, where D represents a three-dimensional region.
  • This participant also notes that the iterated integral can be expressed as ∫ₑᶦ∫ₗᶜ∫ₐᵇ dx dy dz.
  • A later reply agrees with the notion that ∫d³x and ∫∫∫dx₁dx₂dx₃ are equivalent, sharing a personal anecdote about using this notation to indicate dimensionality.

Areas of Agreement / Disagreement

Participants express differing views on the notations, with some asserting they are equivalent while others highlight the less common usage of ∫d³x. The discussion remains unresolved regarding the preference or implications of using one notation over the other.

Contextual Notes

The discussion does not clarify the assumptions behind the notations or their specific contexts of use, leaving some ambiguity regarding their applications in different mathematical scenarios.

Moayd Shagaf
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So My Question Is Simple, But It confuse me too much!
What Is Difference between the notation ∫d3x and ∫∫∫dxdydz ?
 
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nothing...
 
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Likes   Reactions: jasonRF and Moayd Shagaf
Moayd Shagaf said:
What Is Difference between the notation ∫d3x and ∫∫∫dxdydz ?
Have you seen the first form somewhere? The more usual form for a triple integral like this would be ##\int_D dV##, where D is some three-dimensional region. As an iterated integral, it might be written in a form such as ##\int_e^f~\int_c^d~\int_a^b dx~dy~dz##.
 
Dr Transport said:
nothing...
I completely agree.
##\int\, d^3x = \int \int \int \, dx_1 \, dx_2 \, dx_3##
Likewise, an N dimensional integral can be denoted ##\int \, d^Nx##.

I often use this notation myself to remind me how many dimensions I am working in. I picked up the habit from my graduate advisor who used this notation exclusively as far as I can recall.

jason
 

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