How to calculate a composite triple integral with exponential function?
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Drawing
on 11 Apr 2024 at 11:05
Commented: Drawing
on 11 Apr 2024 at 13:19
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.
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Accepted Answer
Torsten
on 11 Apr 2024 at 13:08
Edited: Torsten
on 11 Apr 2024 at 13:15
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 = @(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)
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