Numerical integration over (0, x1)
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Raj Patel
el 21 de Sept. de 2020
Comentada: Raj Patel
el 21 de Sept. de 2020
I am trying to numerical integrate the function. I am not able to solve it. Can anyone help me?
Note: t is a constant over here and limits are from 0 to x1.
Thanks in advance.
Raj Patel.
6 comentarios
Respuesta aceptada
John D'Errico
el 21 de Sept. de 2020
If t is unknown, then you need to use symbolic tools to do the integration.
syms x t
K = 1/((exp(0.014342/(x * t)) - 1)) * (1/(x^4));
int(K,x,[0,1])
ans =
int(1/(x^4*(exp(2066900027383925/(144115188075855872*t*x)) - 1)), x, 0, 1)
MATLAB just returns the integral in the form it was given. I tried Wolfram Alpha, which also agrees it cannot find a solution. There is no assurance that anything you write down has a nice closed form solution.
You have some options. If you had some value for t, then we could write it as:
Kxt = @(x,t) 1./((exp(0.014342./(x * t)) - 1)) .* (1./(x.^4));
foft = @(t) integral(@(x) Kxt(x,t),0,1);
foft(3)
ans =
22003287.386445
foft(1.2)
ans =
1408175.40694754
So while no analytical form is available, we can find a numerical solution. I could have used vpaintegral too.
Finally, you could probably write the problem as a series expansion, but then you would need to consider the domain of convergence, etc.
Más respuestas (1)
Alan Stevens
el 21 de Sept. de 2020
Need to write fun as
fun = @(x) (1./(exp(0.014342./(x*t))-1).*1./x.^4);
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