integrate function

Hey,

i want to integrate the function di on an interval from 1 to infinity. di=(sinh((b.*x)./a)./sinh((pi.*x)./a));

However while using quadgk matlab returns the following error code: Warning: Infinite or Not-a-Number value encountered.

Is there a possibility to change to change the code so maybe that it lowers accuracy however a result is obtained? Or is there another function that evaluates integrals up to infinity?

Thanks in advance.

Answer 1

[Mike Hosea]

The problem has nothing to do with the integrator, rather with the way you have written the integrand:

>> a = 1; b = 1;
>> di= @(x)(sinh((b.*x)./a)./sinh((pi.*x)./a));
>> di(1000)
ans =
   NaN

You're giving the integrator NaN values, so there's not much it, or any other code, can do with that. Try multiplying your integrand numerator and denominator by exp(-pi*x) and simplifying. I get

>> dj= @(x)(exp((b-pi)*x) - exp(-(b+pi)*x))./(1-exp(-2*pi*x))
dj = 
    @(x)(exp((b-pi)*x)-exp(-(b+pi)*x))./(1-exp(-2*pi*x))
>> dj(1000)
ans =
     0
>> quadgk(dj,1,inf)
ans =
   0.051035297097439

-- Mike