# How to calculate the integral of a function with a spline in it

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Renan Kops el 21 de Abr. de 2017
Comentada: Andrew Newell el 25 de Abr. de 2017
Hello Everybody,
So i have a function called FB, and it is the product of a couple of functions
nB = spline(Wavelength,B3);
emi = @(x) 1.989e-6*(10^9*x).^2-0.002;
FB = @(x,T) nB(x).*emi(x)./(x.^5.*(exp((h.*c)./(x.*k.*T))-1))
%integration:
RaBG(Counts) = integral(@(x)FB(x,T),400e-9,720e-9)
nB is a function i must adquire from data. When fitting it with a polinomial function i get a small error which i believe is making me get wrong results, though the code works. I'm trying to fit it with a spline but haven't been able to get the code to work. I also tryied calling FB as this, which didn't work:
FB = @(x,T) ppval(nB,x).*emi(x)./(x.^5.*(exp((h.*c)./(x.*k.*T))-1));
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Renan Kops el 24 de Abr. de 2017
Some of my data is evenly spaced so I can use this, good idea!
Any alternatives for the data that isn't evenly spaced?
John D'Errico el 25 de Abr. de 2017
I'd like to chime in here,but without knowing what wavelength, B3, and G3 are, it is impossible to give a useful answer.

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### Respuestas (1)

Andrew Newell el 24 de Abr. de 2017
Editada: Andrew Newell el 24 de Abr. de 2017
For evenly or unevenly spaced data, you could use the trapezoidal rule (MATLAB function trapz).
Interpolation is also reasonable. How exactly isn't the code working?
I don't see any values assigned to c, k or T. Are you doing that earlier? If so, it would make sense to define
FB = @(x) ppval(nB,x).*emi(x)./(x.^5.* (exp((h.*c)./(x.*k.*T))-1));
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Renan Kops el 25 de Abr. de 2017
Well it is possible, i will try to rescale it.
But, if that was the case, shouldn't i get wrong answers when integrating a 10th degree polinomial or with the Newton-Cotes method? Because both these methods worked and gave me a nice approximation of the real answer (For now i am trying to replicate the results of a paper to check if my code is performing as expected).
Thank you for all the help Andrew.
Andrew Newell el 25 de Abr. de 2017
I'm glad to know that the alternative methods are working!

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