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Is it possible to integrate a shape-preserving curve fitted function ?

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UDIT SARASWAT
UDIT SARASWAT 2018-1-29
I have a discrete set of values for the variable. A polynomial curve fitting leads to deviation at the end points, hence shape-preserving curve fit is employed. Since the function definition changes constantly between pair of nodes, no general equation could be extracted. I need to carry out an integration for the curve within the extreme limits provided in the available data set.

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