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Maximizing the fraction of two integrals using matlab

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  1. Nov 7, 2013 #1
    EDIT:
    I left out something of major importance, I want to maximize with respect to a!

    Good day,

    I've run into an issue in solving a certain problem with matlab, and I was hoping if anyone could help me out. I am relatively new to matlab, so I don't even know if this is possible, but I figured that in principle it should be.

    What I want to do is maximize

    integrals.jpg

    for positive values of a.
    With the calculus I know, I can't evaluate these integrals, so I have no applicable formula's so I am pretty stuck at this point. I tried using mathematica, and although it can evaluate the integrals, it cannot maximize the fraction. So instead I figured I should use matlab (which I also have to my disposal) to do so instead, but I simply don't know how.


    I don't get much further than defining the integrals, as
    fun1 = @(x) x.^2./(exp(x)-1);
    fun2 = @(x) x.^3./(exp(x)-1);

    Could anyone help me out?

    Kind regards
     
    Last edited: Nov 7, 2013
  2. jcsd
  3. Nov 7, 2013 #2

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    Given the Mathematica can solve the integrals - then just use a as a parameter and plot the ratio for a running from 0 to 100 by steps of 1 - and look at the plot.

    Mathematica will be a better tool for this type of work than Matlab.
     
  4. Nov 21, 2013 #3

    kreil

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    Gold Member

    That's not true at all, MATLAB can handle problems like this just fine.

    1. Define the functions. You got this part already.

    Code (Text):

    fun1 = @(x) x.^2./(exp(x)-1);
    fun2 = @(x) x.^3./(exp(x)-1);
     
    2. Define the function with a parameter.

    Code (Text):

    q = @(a) integral(fun1,a,Inf)./integral(fun2,a,Inf);
     
    3. Plot the results and read the maximum off the plot.

    Code (Text):

    for j=0:100
        Q(j+1) = q(j);
    end
    plot(0:100,Q)
     
    The answer is 0, which is rather intuitive when you think about it.
     

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