# Numerical integration over (0, x1)

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Raj Patel on 21 Sep 2020
Commented: Raj Patel on 21 Sep 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.
Raj Patel.

Raj Patel on 21 Sep 2020
"t" is an unknown constant. What shall I use to integrate it if I cannot use integral?
Raj Patel on 21 Sep 2020
I tried using int(function) to solve, but I am still not getting an answer.
Raj Patel on 21 Sep 2020
I tried using int(function) to solve, but I am still not getting an answer.

John D'Errico on 21 Sep 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.

#### 1 Comment

Raj Patel on 21 Sep 2020
Thank you John. I appreciate your effort and time.

Alan Stevens on 21 Sep 2020
Need to write fun as
fun = @(x) (1./(exp(0.014342./(x*t))-1).*1./x.^4);

#### 1 Comment

Raj Patel on 21 Sep 2020
Thanks Alan.