1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Approximate integration

  1. Apr 29, 2009 #1


    User Avatar
    Science Advisor
    Gold Member

    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


    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook