Consider a data set with some numerical uncertainty in the y-values, such as the following
g[x_] := x^3
data = Table[{x, Around[g[x], RandomReal[{0, .1}]]}, {x, 0, 2, .1}]
I want to numerically integrate the data and find the uncertainty in the result. The only way I know how to numerically integrate the data in Mathematica is to first interpolate, such as
interp = Interpolation[data]
int[y_] := NIntegrate[interp[x], {x, 0, y}]
When I do so with the data with uncertainty, however, I get
The integrand InterpolatingFunction[...] has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,0.1}}
Is Mathematica capable of doing these numerical integrals with uncertainties? And if so, is it documented how it estimates the uncertainty? If not, is there a standard method/workaround to this (I guess something like Monte Carlo resampling?)
Interpolation
is making any use of your uncertainties and thus your integral will make no use of your uncertainties, perhaps reference.wolfram.com/language/howto/… might be of interest to you, but I still don't think your uncertainties are going to be directly applicable toNIntegrate
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