How do I integrate this multivariable function over just one variable?
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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.
. (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.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.
采纳的回答
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 个评论
L'O.G.
2022-3-8
Walter Roberson
2022-3-8
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
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