[VA] SRC #012d - Then and Now: Area

[Albert Chan]

(01-12-2023 08:37 PM)J-F Garnier Wrote:  (MAIN= 2.07662636775 TINY= 7.1976193049E-5 )

I still think the tiny area is not OP were asking ...
Anyway, we can confirm TINY area, assuming the dot look like an ellipse.
Or, we think of half ellipse area, with minor axis = FNF(center)

>f, g                                            ! (ymax, ymin), from JFG code
 -4.04921226445      -4.08514674762
>c = (f+g)/2 @ a = (f-g)/2 @ b = fnf(c)
>s = pi/2 * a * b                          ! half ellipse area
>s
 7.19760843094E-5

Almost 6 digits accuracy. Not bad for 1 function evaluation!

2 more function evaluations, we gain another digit accuracy.
Simpson's weight, for 5 points = [1, 4, 2, 4, 1] / 12

There is no need to evaluate odd points. FNF(y) matched ellipse numbers.
S1=0, we might as well go for Boole's rule : S2 + (S2-S1)/(16-1) = 16/15 * S2

>h = sqrt(0.75) * b
>s + ((fnf(c-a/2)-h) + (fnf(c+a/2)-h)) * 4/12 * 16/15 * (2*a)
7.19761691227E-5