Numerical integration over (0, x1)
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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 个评论
John D'Errico
2020-9-21
PLease don't insert a picture of code. If it were text, I could just copy your function into MALTAB to look at it. As it is, then I need to retype it, for no good reason. And while this is a simple case, why in the name of god and little green apples would you want to make it more difficult for someone too help you?
John D'Errico
2020-9-21
Next, is t a known constant? Does it have some value? What is it? If not, then you cannot use integral to integrate a function with a symbolic parameter.
Raj Patel
2020-9-21
Raj Patel
2020-9-21
Raj Patel
2020-9-21
Raj Patel
2020-9-21
采纳的回答
John D'Errico
2020-9-21
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.
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