tf called my attention on the paper A mathematical model for the determination of total area under glucose tolerance and other metabolic curves by MM Tai, pulished in Diabetes Care, Vol 17, Issue (2) 152–154. According to the abstract:
In Tai’s Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve. Validity of the model is established by comparing total areas obtained from this model to these same areas obtained from graphic method (less than +/- 0.4%). Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin.
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