How can I integrate this function?

Please, I have been trying to simulate the following functions using MATLAB. But I am still unable to get it correctly. The functions are given below;

where;

This is the code I have written following the approach discussed by Star Strider for a similar problem. Any idea on how to make the code works?

x = 2000000; T = 1; a = 4;L = 0.000159; B = 50;
syms r w
firstint = @(w) integral(@(r) (acos (((r.^2) + (w.^2) - (B.^2))/(2 * w * r))* ((2*L * r)/(1+((r.^a)/(x*T))))), w-B, w+B, 'ArrayValued',1);
secondint = @(w) (1-(firstint(w))).*w;
answer = integral(secondint, B, Inf);
D = exp (-2 * pi * L * answer);
final = A * D;

Answer 1

[Cris LaPierre]

The approach you are taking is numeric, so don't declare symbolic variables.

x = 2000000; T = 1; a = 4;L = 0.000159; B = 50;
firstint = @(w) integral(@(r) (acos (((r.^2) + (w.^2) - (B.^2))/(2 .* w .* r))* ((2*L .* r)/(1+((r.^a)/(x.*T))))), w-B, w+B, 'ArrayValued',1);
secondint = @(w) (1-(firstint(w))*w);
answer = integral(secondint, B, Inf, 'ArrayValued',1)

This does give a warning:

Warning: Minimum step size reached near x = 3.24519e+30. There may be a singularity, or the tolerances may be too tight for this problem.

You can look into the options for tolerances of integral here.

[Sam Oke]

Thanks you for your answer. It helped a lot!

Please if I want to follow analytical approach, how do I do about it?

[Cris LaPierre]

You would need to use a symbolic approach, including functions designed to work with symbolic equations (int).