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

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.

Answer 1

[Walter Roberson]

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])

[L'O.G.]

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

[Walter Roberson]

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