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The curve was studied by Pierre de Fermat in his 1659 treatise on quadrature. In it, Fermat computes the area under the curve and (without details) claims that the same method extends as well to the cissoid of Diocles. Fermat writes that the curve was suggested to him "ab erudito geometra" [by a learned geometer]. [16]
Taking an example, the area under the curve y = x 2 over [0, 2] can be procedurally computed using Riemann's method. The interval [0, 2] is firstly divided into n subintervals, each of which is given a width of 2 n {\displaystyle {\tfrac {2}{n}}} ; these are the widths of the Riemann rectangles (hereafter "boxes").
A classification model (classifier or diagnosis [7]) is a mapping of instances between certain classes/groups.Because the classifier or diagnosis result can be an arbitrary real value (continuous output), the classifier boundary between classes must be determined by a threshold value (for instance, to determine whether a person has hypertension based on a blood pressure measure).
The area under the effect curve (AUEC) is an integral of the effect of a drug over time, estimated as a previously-established function of concentration. It was proposed to be used instead of AUC in animal-to-human dose translation, as computer simulation shows that it could cope better with half-life and dosing schedule variations than AUC.
While the Riemann integral considers the area under a curve as made out of vertical rectangles, the Lebesgue definition considers horizontal slabs that are not necessarily just rectangles, and so it is more flexible. For this reason, the Lebesgue definition makes it possible to calculate integrals for a broader class of functions.
PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers, and transcendental functions. [3]
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Archimedes in his The Quadrature of the Parabola used the sum of a geometric series to compute the area enclosed by a parabola and a straight line. Archimedes' theorem states that the total area under the parabola is 4 / 3 of the area of the blue triangle. His method was to dissect the area into infinite triangles as shown in the ...