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Approximate integration

  • Thread starter Matterwave
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  • #1
Matterwave
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Homework Statement


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].


Homework Equations





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?
 

Answers and Replies

  • #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:
 
  • #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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