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How to calculate a composite triple integral with exponential function?

2 vues (au cours des 30 derniers jours)
Drawing
Drawing le 11 Avr 2024
Commenté : Drawing le 11 Avr 2024
Hello! I have a composite triple integral, but i cant find a proper approach to calculate it.
,where the variables are "r","s","l".
r0 is a known constant.
I try to use integral3, but the exp() and the variable 'l' for the lower bound of the integral makes it hard to calculate.
Is there any other matlab function that is suitable to solve this composite triple integral? I would appreciate it if anyone could give me some advice.
  6 commentaires
Drawing
Drawing le 11 Avr 2024
Thank you Torsten! I have added that "r0 is a known constant."
Drawing
Drawing le 11 Avr 2024
Thank you Dyuman Joshi! I have added my tries, and i also have the Symbolic Math Toolbox.

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Torsten
Torsten le 11 Avr 2024
Modifié(e) : Torsten le 11 Avr 2024
Setting l, r and s to zero will cause problems because you divide by these variables.
But also changing
integral2(@(s,l)arrayfun(@(s,l)fun(s,l),s,l),0,Inf,0,r0)
to
integral2(@(s,l)arrayfun(@(s,l)fun(s,l),s,l),1e-4,Inf,1e-4,r0)
does not help.
Thus try to check theoretically whether your integral exists at all.
r0 = 100;
fun_inner = @(s,l)integral(@(r)1./(1+s./r.^2).^2.*r,l,r0)
fun_inner = function_handle with value:
@(s,l)integral(@(r)1./(1+s./r.^2).^2.*r,l,r0)
fun = @(s,l)exp(-s)./s .*exp(fun_inner(s,l)).* 1./(1+s./l.^2)
fun = function_handle with value:
@(s,l)exp(-s)./s.*exp(fun_inner(s,l)).*1./(1+s./l.^2)
value = integral2(@(s,l)arrayfun(@(s,l)fun(s,l),s,l),0,Inf,0,r0)
Warning: Inf or NaN value encountered.
Warning: The integration was unsuccessful.
value = NaN

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