Integrating Norm in Unit Ball in Rn-2

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    Integrating Norm
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Discussion Overview

The discussion revolves around the integration of the function |x|² with respect to the vector x within the unit ball in Rn-2. Participants explore methods for evaluating this integral, including the application of generalized spherical coordinates and Fubini's Theorem.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant presents the integral \int|x|² with respect to the vector x in the unit ball in Rn-2 and expresses difficulty in finding a solution.
  • Another participant suggests the use of generalized spherical coordinates as a potential approach.
  • A further participant questions whether |x|² simplifies to r² in this context and requests clarification on generalized spherical coordinates.
  • One participant later indicates they found an alternate method to approach the problem, but does not elaborate on this method.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants explore different methods without resolving the initial query about the integral.

Contextual Notes

Some assumptions regarding the application of generalized spherical coordinates and the specifics of the integral's evaluation remain unaddressed. The discussion also does not clarify the implications of the change of variables mentioned by the initial poster.

Matthollyw00d
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\int|x|2 with respect to the vector x in the unit ball in Rn-2

I'm dealing with volumes of unit balls in Rn and after applying a change of variable to the last 2 components and Fubini's Theorem, I get that integral and can't find a way to integrate it. Any help on this?
 
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Generalized spherical coordinates.
 
Would that just make |x|2=r2? I've never worked with generalized spherical coordinates before, so could you elaborate a bit?
 
Nevermind, I found an alternate way.
 

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