How do I integrate this multivariable function over just one variable?
8 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
L'O.G.
le 8 Mar 2022
Commenté : Walter Roberson
le 8 Mar 2022
How do you do you do the following like
. (My actual function is more complicated, but this should suffice, I think.) Here, t, r, and x are all variables, with x just being used for purposes of the integration.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/919224/image.png)
I tried something like
a = 0;
b = 2;
for t = 1:10
sum = 0;
for r = 1:10
f = @(x) sin(r*t*x.).^2;
sum = sum + f;
end
0.5*integral(sum,a,b)
end
But I can't add the function handle and am not sure if the procedure is even correct. How do I do this? For every t there should be many r.
0 commentaires
Réponse acceptée
Walter Roberson
le 8 Mar 2022
Well, you can
a = 0;
b = 2;
for t = 1:10
sum = @(x) zeros(size(x));
for r = 1:10
f = @(x) sin(r*t*x).^2;
sum = @(x) sum(x) + f(x);
end
0.5*integral(sum,a,b)
end
This is not a great integral; t and r should be finer steps, and you should be taking into account dt and dr and you should probably be using trapz() or cumtrapz()
If you can use symbolic work it goes much easier:
syms r t x
a = 0;
b = 2;
F(t) = int(sin(r*t*x).^2, x, a, b)
To be equivalent to your proposed code this should probably be integrated over r = 1 to 10
syms r t x
a = 0;
b = 2;
F(t) = int(int(sin(r*t*x).^2, x, a, b),r,1,10)
fplot(F, [1 10])
2 commentaires
Walter Roberson
le 8 Mar 2022
Evaluate the function over a (possibly multidimensional) grid, trapz() or cumtrapz() over appropriate dimensions.
This would mostly be of use if you wanted to be able to output that data separately; otherwise you would just use integral() or integral2() or integral3() or https://www.mathworks.com/matlabcentral/fileexchange/47919-integraln-m
Plus de réponses (0)
Voir également
Catégories
En savoir plus sur Numerical Integration and Differentiation dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!