Integration Issues: How to Join Parts and Techniques

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Discussion Overview

The discussion revolves around integration techniques, specifically in the context of electromagnetism. Participants are examining a particular integration problem related to finding the electric field on a disk, as presented in a textbook example.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the transition between parts of the integration process and questions the treatment of the factor of 2.
  • Another participant suggests that the expression 2r(dr) is being substituted with d(r^2), likening it to a u-substitution, but notes unfamiliarity with this specific approach.
  • A participant confirms they are studying electromagnetism and identifies the example as related to calculating the electric field on a disk, indicating a struggle with the integration process.
  • One participant proposes that using the substitution u = r^2 would allow for replacing 2rdr with du, suggesting that the original notation may have been simplified.
  • Another participant acknowledges the substitution and expresses gratitude for the clarification, indicating a better understanding of the integration technique.
  • A later reply comments on the notation, questioning the meaning of d(r^2) and clarifying that it equals 2r dr, suggesting a potential misuse of notation.

Areas of Agreement / Disagreement

Participants exhibit a mix of confusion and clarification regarding the integration technique, with no consensus reached on the treatment of the factor of 2 or the notation used in the integration process.

Contextual Notes

There are unresolved questions regarding the assumptions made in the integration steps and the notation used, particularly concerning the treatment of differentials and substitutions.

Prologue
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I am not sure exactly what is happening between the first part and second part. What happens to the 2?

Also, what technique do you use to integrate after that? I am a little unsure as to what slick moves are being used here. Any help is appreciated.

http://img511.imageshack.us/img511/2091/14157612rc6.jpg
http://g.imageshack.us/g.php?h=511&i=14157612rc6.jpg
 
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I don't understand the context this is in but it looks like the 2r(dr) is being replaced by the substitution d(r^2) = 2r(dr) (this resembles usub, but I've never encountered this before). The denominator in the first step is just brought up top with a negative exponent. From step two to three, it looks like polynomial integration.

Hmm are you learning electromagnetism right now?
 
Yep electromagnetism. It is out of the first chapter on the subject in Serway and Jewett. The example is for finding the electric field on a disk.

I am really stuck on that two, it seems like it has to be a mistake. There is probably some perspective I am missing here, that dr*2r=dr^2, but I am not seeing it now.

I can work it out fine with a substitution, but I really like to understand everything I encounter, and this doesn't mesh well.
 
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If you let u = r^2, then you would replace 2rdr with du, wouldn't you?
Here, they have just not bothered renaming r^2.
 
Big-T said:
If you let u = r^2, then you would replace 2rdr with du, wouldn't you?
Here, they have just not bothered renaming r^2.

Perfect, yep that is the angle I was missing. Of course I made the substitution u=x^2 +r^2 so du=2rdr. So thinking this way, keep going du=d(x^2+r^2)=d(r^2) etc.

Thank you for the advice.
 
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Prologue said:
There is probably some perspective I am missing here, that dr*2r=dr^2, but I am not seeing it now.

It's kind of an abuse of notation. What's d(r^2)? It's the differential of r^2, which equals 2r dr.
 

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