Symbolic math integrals not solving at all

47 vues (au cours des 30 derniers jours)
Florian Rössing le 30 Avr 2021
Commenté : Taw Tha le 24 Avr 2023
Hi all, I am playing around with functions and the symbolic math toolbox.
I want to calculate an integral of a difficult function:
syms t t0 tau x;
syms l(t,t0,tau);
l(t,t0,tau)= exp(-1/2*exp(-(t-t0)/tau));
syms f(t,t0,tau);
f(t,t0,tau)= exp(-1/2*((t-t0)/tau));
syms p(t,t0,tau);
p(t,t0,tau)=l(t,t0,tau)*f(t,t0,tau);
It can not integrate p directly, which is not that difficult, wolfram alpha does is. But anyhow, I'll help a little and do the substitution:
p=tau*subs(p,(t-t0)/tau,x)
int(p,x,-inf,inf)
But it still just comes up with nothing. It just puts out a formated version of my input instead of calculating the integral.
sqrt(2*pi)*tau
Did I use the toolbox wrong or is it just not that powerfull?
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Walter Roberson le 29 Juil 2021
When I take the expression over to Maple and convert the exp() into sinh cosh, then Maple is able to integrate the system. However, I do not seem to be able to do the same thing for MATLAB.

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Réponse acceptée

Tanmay Das le 29 Juil 2021
Your function has no obvious closed form integral. You need to switch to numeric integration, such as with integral() or vpaintegral() which will require you to have a numeric value for x. Similar question has already been answered here:
Also, the same is mentioned in the Tips Section of the int documentation:
You can go through the documentations on integral and vpaintegral to try integrate the same function:
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Taw Tha le 24 Avr 2023
Thank you everyone here, I would also like to contribute that simplify('Steps', \*int steps\*)
intFuncky = simplify(int((sqrt(tao^2 - (t-tao)^2) * (t-tao)^2),t,0,2*tao),"Steps",100)
or
intFuncky = simplify(int(( f ,x ,a, b), "Steps" ,100);%100 chosen as a small steps count medium is 400 steps
matlab 2022b

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