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
