MATLAB: How to integrate a vector-valued function

MATLABnumerical integration

I am trying to calculate the attached integral. I have data as vectors r and f(r) tht I load as r and fr, respectively.. The vector x should have the same range as r. Is the following correct? I'm not sure how I should incorporate the fact that f(r) is a function of r, or how the integral depends on x as well.
I try
x = linspace(0.05,17.95,180)';
fun = @(x,r) (r.^2).*(fr-1).*sin(x.*r)./(x.*r);
eq1 = integral(@(r) fun(x,r),0,r(end),'ArrayValued',1);
eq2 = cumtrapz(r,(r.^2).*(fr-1).*sin(x.*r)./(x.*r));
But I get two different answers. Again, r and fr (= f(r)) are both vectors of numbers. Is either eq1 or eq2 one correct? Is neither? I have limited understanding of anonymous functions and numerical integration in MATLAB.

Best Answer

You need to integrate this function w.r.t. 'r' so you shouldn't use x as a vector in your code. Both of your approaches seem to be doing what you might not intend to do. Check this code, it shows how to do this with integral and trapz. Both will give similar results.
R = linspace(1, 100, 1000); % example r
FR = exp(-R); % example fr
x = linspace(0.05,17.95,180)';
fr = @(r) interp1(R, FR, r, 'pchip');
integrand = @(r,x) r.^2.*(fr(r)-1).*sin(x.*r)./(x.*r);
fx_int = @(x) integral(@(r) integrand(r,x), 0, max(R));
fx_int_v = zeros(size(x));
for i=1:numel(x)
    fx_int_v(i) = fx_int(x(i));
end
fx_trapz = @(x) trapz(R, integrand(R, x));
fx_trapz_v = zeros(size(x));
for i=1:numel(x)
    fx_trapz_v(i) = fx_trapz(x(i));
end
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