How do I integrate this multivariable function over just one variable?

Question

L'O.G. 2022-3-8

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https://ww2.mathworks.cn/matlabcentral/answers/1666989-how-do-i-integrate-this-multivariable-function-over-just-one-variable

评论： Walter Roberson 2022-3-8

采纳的回答： Walter Roberson

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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.

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.

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Answer 1

Walter Roberson 2022-3-8

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在 MATLAB Online 中打开

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
ans = 5.0512
ans = 4.9580
ans = 5.0476
ans = 5.0045
ans = 4.9769
ans = 5.0196
ans = 4.9978
ans = 4.9824
ans = 5.0096
ans = 4.9951

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)

F(t) =

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)

F(t) =

fplot(F, [1 10])

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L'O.G. 2022-3-8

Thank you. Is there a cleaner way to do this using trapz or cumtrapz, like you alluded to?

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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