Maximizing the fraction of two integrals using matlab

Tags:
1. Nov 7, 2013

Verdict

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

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. Nov 7, 2013

UltrafastPED

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.

3. Nov 21, 2013

kreil

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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