Approximating an E&M Integral with Calculus

[Matterwave]

Homework Statement

This is technically an E&M question, but I've reduced it to a calculus problem. Basically I have to evaluate:

$$B_0(\int_{-H_{max}}^{H_{max}}{tanh(\frac{H+H_c}{H_0})dH - \int_{-H_{max}}^{H_{max}}{tanh(\frac{H-H_c}{H_0})dH)$$

Where $$H_{max}>>H_C, H_0$$.

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?

 

[tiny-tim]

Hi Matterwave!

Are H_c and H₀ constants?

If so, that's just ∫tanh(Ax + b) dx …

and ∫tanh is ln(cosh)

 

[D H]

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 H_max>>H_c , H₀ to arrive at an approximate value.