Calculus- Area between two curves (minimize it)

In summary, to minimize the area between the two curves, you need to integrate between k=0 and k=pi/dx, and differentiate with respect to Eb.
  • #1
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Hi,

This is my first question here, so please apologise me if something is amiss.
I have two curves such that Wa = f(k,Ea,dxa) and Wb = f(k,Eb,dxb). I need to minimize the area between these two curves in terms of Eb in the bounded limit of k=0 and k=pi/dx. So to say, all the variables can assume any value, and then I can only alter Eb to minimize the area between these two curves.

I have tried integrating both the curvesbetween k=0 and k=pi/dx, and differentiating with respect to Eb and equating it to 0. This does not work.
I also thought about integrating (summing) the distance between the two curves, bu that results in the case above.

Do I need to put a constraint function?

Please feel free to ask if any clarification is needed. I have tried to simply my case, and that may have resulted in some ambiguities.

Thank you
 
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  • #2
I don't understand what you mean by "f(k, Ea, dxa)" and "f(k,Eb, dxb)". I would expect something of the form "f(x)" and "g(x)" with boundary values on x. I might assume that your "k" is my "x" but what are Ea, Eb, dxa, and dxb?
 
  • #3
Hi,
So, both the functions represent the dispersion realtions of two models. So, the "x" and "y" axes whole plotting represent angular frequency (W) and wave number (k), respectively. Wa and Wb represent the angular frequencies of model a and model b, respectively.
Ea,Eb represent Young's moduli of models a and b, and dxa,dxb represent the cell discretization lengths in model a and b, repectively. These are not constants in the sense that can be changed. It is analogous to saying that you can change the parameters of the models.
 

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