MATLAB: Numerical Integration in Matlab

numerical integration

I wanted to solve a numerical integral of the following equation:

fun = ((x.^4 .* exp(x))) ./ ((exp(x) - 1) .* (exp(x) - 1) );

The limits are from: 0 to Inf

Can anyone ehelp me here?

Thanks in advance.

Best Answer

If you have symbolic toolbox

syms x
y = ((x.^4 .* exp(x))) ./ ((exp(x) - 1) .* (exp(x) - 1) );
I = int(y, x, 0, inf)

Result

>> I
I =
(4*pi^4)/15
>> double(I)
ans =
   25.9758

Related Solutions

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

MATLAB: Numerical integration in MATLAB

Try this:

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')

producing:

Since both ‘c’ and ‘fun’ are functions of ‘T’, they need to be coded as such.

Best Answer

Related Solutions

MATLAB: Numerical Integration In Matlab

MATLAB: Numerical integration in MATLAB

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