Numerical Integral in MatLab using integral command

Question

I am trying to compute the value of this integral using Matlab enter image description here

Here the other parameters have been defined or computed in the earlier part of the program as follows

N = 2;
sigma = [0.01 0.1];
l = [15];
meu = 4*pi*10^(-7);
f = logspace ( 1, 6, 500);
w=2*pi.*f;
for j = 1 : length(f)
q2(j)= sqrt(sqrt(-1)*2*pi*f(j)*meu*sigma(2));
q1(j)= sqrt(sqrt(-1)*2*pi*f(j)*meu*sigma(1));
C2(j)= 1/(q2(j));
C1(j)= (q1(j)*C2(j) + tanh(q1(j)*l))/(q1(j)*(1+q1(j)*C2(j)*tanh(q1(j)*l)));
Z(j) = sqrt(-1)*2*pi*f(j)*C1(j);
Apprho(j) = meu*(1/(2*pi*f(j))*(abs(Z(j))^2));
Phi(j) = atan(imag(Z(j))/real(Z(j)));
end

%integration part
c1=w./(2*pi);
rho0=1;
fun = @(x) log(Apprho(x)/rho0)/(x.^2-w^2);
c2= integral(fun,0,Inf);
phin=pi/4-c1.*c2;

I am getting an error like this enter image description here

could anyone help and tell me where i am going wrong.thanks in advance

You create Apphro in the for loop as an array, but then you use it in the integration as a function. — David
– David, Commented Apr 24, 2015 at 22:35
my objective is to calculate the integral part-to do this I need to define Apprho function. — shrey
– shrey, Commented Apr 24, 2015 at 23:39

Jeff Irwin · Accepted Answer · 2015-04-25 03:48:11Z

1

Define Apprho in a separate *.m function file, instead of storing it in an array:

function [ result ] = Apprho(x)
%
% Calculate f and Z based on input argument x
%
% ...
%
meu = 4*pi*10^(-7);
result = meu*(1/(2*pi*f)*(abs(Z)^2));
end

How you calculate f and Z is up to you.

MATLAB's integral works by calling the function (in this case, Apprho) repeatedly at many different x values. The x values called by integral don't necessarily correspond to the 1: length(f) values used in your original code, which is why you received errors.

answered Apr 25, 2015 at 3:48

Jeff Irwin

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