Integrating from 0 to 1 in r, z and θ

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Discussion Overview

The discussion revolves around the integration of a volume element in cylindrical coordinates, specifically integrating from 0 to 1 in the radial direction (r), from -1 to 1 in the vertical direction (z), and from 0 to 2π in the angular direction (θ). The context includes formatting issues related to LaTeX representation in the forum.

Discussion Character

  • Meta-discussion

Main Points Raised

  • Participants present the limits of integration for r, z, and θ, along with the volume element dV expressed in cylindrical coordinates.
  • One participant expresses confusion about the formatting of their LaTeX input, suggesting it may have been a glitch in the preview feature.
  • Another participant confirms that the formatting issue was related to the preview feature and offers a solution to refresh the browser for proper LaTeX rendering.
  • There is a light-hearted acknowledgment of poor LaTeX skills from one participant.

Areas of Agreement / Disagreement

Participants generally agree on the formatting issues related to LaTeX and the integration setup, but there is no substantive disagreement on the mathematical content itself.

Contextual Notes

Limitations include potential misunderstandings of LaTeX formatting and the need for browser refresh to properly view mathematical expressions.

{~}
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[tex] 0 \leq r \leq 1<br /> -1 \leq z \leq 1<br /> 0 \leq \theta \leq 2\pi<br /> <br /> \int\int\int dV<br /> <br /> where dV = r dr d/theta<br /> <br /> r = 1 - z<sup>2</sup>[/tex]

weird huh?
 
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looks like it was just the preview that was glitching, my bad
 
{~} said:
[tex] 0 \leq r \leq 1<br /> -1 \leq z \leq 1<br /> 0 \leq \theta \leq 2\pi<br /> <br /> \int\int\int dV<br /> <br /> where dV = r dr d/theta<br /> <br /> r = 1 - z<sup>2</sup>[/tex]

weird huh?

[tex] 0 \leq r \leq 1<br /> -1 \leq z \leq 1<br /> 0 \leq \theta \leq 2\pi[/tex]

[tex] \int\int\int dV[/tex]


where [tex]dV = r dr d{\theta}[/tex]

[tex] r = 1 - z^2[/tex]

Better?
 
I changed some things to get it formatted a little better, but it looks like it was just the preview "feature" that was getting you. Glad you figured it out.
 
thanks now you know how bad my latex is
 
hi {~}! :smile:

in case you haven't yet found out, click "Refresh" (on your browser) after clicking "Preview" … that'll update the LaTeX images :wink:
 

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