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Approximate integration

  1. Apr 29, 2009 #1

    Matterwave

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    1. The problem statement, all variables and given/known data
    This is technically an E&M question, but I've reduced it to a calculus problem. Basically I have to evaluate:

    [tex]B_0(\int_{-H_{max}}^{H_{max}}{tanh(\frac{H+H_c}{H_0})dH - \int_{-H_{max}}^{H_{max}}{tanh(\frac{H-H_c}{H_0})dH)[/tex]

    Where [tex]H_{max}>>H_C, H_0[/tex].


    2. Relevant equations



    3. The attempt at a solution

    I'm looking at this and I have no idea how to go about approximating this integral...I suppose I could just brute force the integrals and keep all the H_max and stuff, and then later see if i can approximate something...but the expressions are really quite long and I'd like to avoid that if I can. Is there a way?
     
  2. jcsd
  3. Apr 29, 2009 #2

    tiny-tim

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    Hi Matterwave! :smile:

    Are Hc and H0 constants?

    If so, that's just ∫tanh(Ax + b) dx …

    and ∫tanh is ln(cosh) :wink:
     
  4. Apr 29, 2009 #3

    D H

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    You can eliminate the second integral (it's just the additive inverse of the first; prove it). Per tiny-tim's hint, you can compute the integral. Simplify and finally use the fact that Hmax>>Hc , H0 to arrive at an approximate value.
     
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