Is this not just the trapezoidal rule for numeric integration?
https://en.wikipedia.org/wiki/Trapezoidal_rule
It's not even a particular good choice for the specific problem (glucose curve) because the trapezoidal rule will systematically underestimate the true area when the curvature is always negative. Simpson's rule is almost always a better choice:
https://en.wikipedia.org/wiki/Simpson%27s_rule
Fun fact: although the method is attributed to the 18th century mathematician Simpson, Kepler is known to have used it in the 17th century.
Re:The Birth of Calculus (1986) [video]
by 29athrowaway on Monday April 27, 2020 @08:12PM
(#23001828)
Tai's "integration" method also has references to previous, similar work, and has 293 citations. You can buy the paper for $35.
Academia in a nutshell.
https://math.berkeley.edu/~ehallman/math1B/TaisMethod.pdf
> RESEARCH DESIGN AND METHODS— 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