MATLAB: Numerican Integration in Matlab

integrationnumerical

I need some help solving numerical integration.

The integral is:

fun = @(x) (x .* (exp(x) ./ (exp(x) – 1).^2) .* ((asind(0.0003 .* T .* x)).^2 ./ sqrt(1 – (0.0003 .* T .* x).^2))); Note: asind = sin^-1(….) –> (I am not sure if this is correct)

C = @(T) integral(fun, 0, 517.39 ./ T);

The limit of x is from: x = 0 to x = (500/T)

T ranges from (1 – 1000) (which is T = logspace(0, 3))

Can anyone help me solve this integral. I want to plot a loglog plot of (C as a function of T). I am getting some errors which I am not able to overcome.

Thanks in advance.

Raj.

Best Answer

See my Answer to your duplicate Question: Numerical Integration In Matlab

Related Solutions

MATLAB: Are there speedier alternatives to the mode function

You could attempt to take advantage of the fact that elements in 'poss' are positive integers and can be used as indices. However, I tend to doubt that in a span of only 12 elements in each column of 'poss' the following code could outperform Mathworks' 'mode', but you can try it and see.

   subs = [poss(:),reshape(repmat(1:4^12,12,1),[],1)];
   F = max(accumarray(subs,1,[4,4^12]),[],1);
   evenposs = poss(:,F==x); % <-- Or do you mean F<=x?

MATLAB: Numerical Integration In Matlab

The integral function will produce one value for the specific limits of integration. To create a vector from its outputs, a loop is necessary.

Try this:

fun = @(x) (x .* (exp(x) ./ (exp(x) - 1).^2) .* ((asind(0.0003 .* 1 .* x)).^2 ./ sqrt(1 - (0.0003 .* 1 .* x).^2)));
T = logspace(0, 3);
C = @(T) integral(fun, 0, 517.39 ./ T);
for k = 1:numel(T)
    Cint(k) = C(T(k));
end
figure
plot(T, Cint)
grid

Best Answer

Related Solutions

MATLAB: Are there speedier alternatives to the mode function

MATLAB: Numerical Integration In Matlab

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