How can I integrate this function?

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Sam Oke
Sam Oke 2018-11-16
评论： Cris LaPierre 2018-11-28
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;

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Cris LaPierre
Cris LaPierre 2018-11-17
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.
  2 个评论
Sam Oke
Sam Oke 2018-11-28
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
Cris LaPierre 2018-11-28
You would need to use a symbolic approach, including functions designed to work with symbolic equations (int).

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