Integrating a series of point value in Mathcad 1

[Pinco]

Hallo Everybody
I'm Pinco and i'm new in this forum.
I have a question for you guys:
i would like to integrate a function, basically the Stefann-Boltzmann function. over a finite range of wavelenghts with Mathcad 14.
In this function i would also like to include the so-called emissivity, which is different from material and also dependent on the wavelength.
Usually i hold the emissivity constant to a certain value, but this is not completely correct because its value changes as function of the wavelength.
Now my question is if there is a way in Mathcad to integrate a function where also there is a series of point value, something like this:

integral (x₁ to x₂) (f(x)* emissivity(x)) dx

where basically for every x (wavelength) you have a different emissivity.

thanks a lot for your help

 

[IRstuff]

You can resort to classical numerical integration, where the intervals correspond to that of the emissivity data. Another possible choice would be to create a virtual continuous function for the emissivity by embedding the data inside a linterp. So long as the integral operator can get values back for any value of the variable of integration, it should be happy.

TTFN
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[Pinco]

Hi IRstuff
thanks for your valuable suggestions. I'll definitely try the first one (discretizing with a summation over each wavelength).
i have already tried to fit this expression and insert the fitting function in the integral but at the end i get a negative result, so something must definitely be wrong. i'll try to work this out again.

 

[Pinco]

Hi again IRstuff
i forgot to ask you another question. You suggested to do classical numerical integration, but in a way i have already done that with mathcad
by using the Integral operator, which as i explained, doesn't give the opportunity to do what i had in mind. To which operator in mathcad are you
explicitly referring? i have, out of curiosity, tried also the summation operator but the summation operator is not really doing numerical integration
but it is simply adding a function n-times. thanks again

 

[IRstuff]

The integral operator requires a virtually continuous function, which is why I suggested that you wrap your data with some sort of interpolation, which would avoid any issues with the integral. Barring that, a numerical integration would use the summation operator, as we were all taught in school.

TTFN
faq731-376

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