Numerical Integration In Matlab

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Raj Patel 2020-10-13

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https://ww2.mathworks.cn/matlabcentral/answers/612746-numerical-integration-in-matlab

评论： Star Strider 2020-10-27

采纳的回答： Star Strider

I need some help solving numerical integration.

The integral is:

fun = @(x) (x .* (exp(x) ./ (exp(x) - 1).^2) .* ((asind(0.0003 .* 1 .* x)).^2 ./ sqrt(1 - (0.0003 .* 1 .* 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.

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Star Strider 2020-10-13

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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

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Raj Patel 2020-10-27

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Hi Star,

I wanted some help with a Matlab coding. I am trying to integrate a function and this function has a variable T which ranges from 1:1000. How do I get numerical integral for all these values of T and then plot it as a function of T? Could you help me? The Matlab code is:

kb = 1.38 .* 10.^-23;
h = 1.05 .* 10.^-34;
wd = 6.94 .* 10.^13;
vs = 6084;
B1 = 2.7 .* 10.^-19;
B2 = 170;
A1 = 2 .* 10.^-45;
D = 0.004;
c = (h.^2 .* D) ./ (2 .* pi * pi * vs * kb .* T .* T);
T = 1:1000;
fun = @(x) ((x.^4 .* exp((h.*x) ./ (kb .* T))) ./ (((exp((h.*x) ./ (kb .* T))-1).^2) .* ((D.*B1 .* x.^2 .* T .* exp(-B2/T)) + (D.*A1 .* x.^4) + vs)));
K = c .* integral(fun,0,wd)
plot(T, K)

Thanks in advance,

Raj Patel.

Star Strider 2020-10-27

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As always, my pleasure!

I thought we just solvedd that exact problem? I only posted the few lines that changed.

The full code is:

kb = 1.38 .* 10.^-23;
h = 1.05 .* 10.^-34;
wd = 6.94 .* 10.^13;
vs = 6084;
B1 = 2.7 .* 10.^-19;
B2 = 170;
A1 = 2 .* 10.^-45;
D = 0.004;
T = 300;
c = @(T) (h.^2 .* D) ./ (2 .* pi * pi * vs * kb .* T .* T);
fun = @(x,T) ((x.^4 .* exp((h.*x) ./ (kb .* T))) ./ (((exp((h.*x) ./ (kb .* T))-1).^2) .* ((D.*B1 .* x.^2 .* T .* exp(-B2/T)) + (D.*A1 .* x.^4) + vs)));
T = 1:1000;
for k = 1:numel(T)
    K(k) = c(T(k)) .* integral(@(x)fun(x,T(k)),0,wd);
end
figure
plot(T, K)
grid
xlabel('T')
ylabel('K')

It produces the same plot, so I will not re-post it.

This also works (without the loop, using 'ArrayValued'):

c = @(T) (h.^2 .* D) ./ (2 .* pi * pi * vs * kb .* T .* T);
fun = @(x,T) ((x.^4 .* exp((h.*x) ./ (kb .* T))) ./ (((exp((h.*x) ./ (kb .* T))-1).^2) .* ((D.*B1 .* x.^2 .* T .* exp(-B2./T)) + (D.*A1 .* x.^4) + vs)));
T = 1:1000;
K = c(T) .* integral(@(x)fun(x,T),0,wd,'ArrayValued',1);
figure
plot(T, K)
grid
xlabel('T')
ylabel('K')