How to calculate area from noisy points of given function?

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I was asked to calculate area from noisy points of given function (the function can represent any closed abstract shape).

im getting function and take something like 1000 noisy points from that function (randomly given by samples).

I've tried to use sklearn.cluster.kmeans to find 'x' centers points and on them im doing the shoelace formula, but I still dont get the accuracy that i want.

Does someone know if I need to have attention to something in the way I was representing? Or is there much better other way to do that?

*Im using python 3

Thanks for the help.

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