plot(data,#,size,#)

17b4eb89-9c30-4532-bd79-71f794c146b2 24 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

plot(data,#,size,#)

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

Int(f,a,b,n) ... Simpson/Romberg Kernel

Simpson Integrator in the Romberg Transform Domain [0,1] <= [a,b] ...  
... integrates  Smath ainterp(X,Y,x), cinterp(X,Y,x), cubic(x) from  l_p_c_spline f a b n Int w s b a - (34 / 2 w * 1 - (* 14 / 2 w * 1 - (3^* - 12 / + (* a + : w G w s f 12 w * 1 - (2^- (* : α 0 : β 1 : h β α - n / : 14 mat Simpson 13 / h 2 / α G β G + (* h α k h * + G k 1 n 1 - sum * + (* 23 / h * α h 2 / - k h * + G k 1 n sum * + eval : 32 / b a - (* Simpson * 41 line :

The 3 most common Cumulative Integrators . . . [1] FD ... [2] RK's ... [3] ∫f(x)

[1] Finite Differences is very accurate as some kind of yardstick for most, if not all applications.

[2] must be tested vs FD to insure long range convergence.

[3] works well, but not for all demand s ... this particular parametric f(x,) ... unexplained failure.

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α 1523043253 - 27354.7 - 43256.75 25388.3 - 40061 mat :

Fréchet: extreme value-II x f α 1 el α 2 el x α 4 el - (/ (α 5 el^* α 2 el x α 4 el - (/ (α 3 el^- exp * α 6 el + :

data Σ Finite differences Cumul Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

data U 013 0.1 range : i 1 U rows range vy i el U i el f eval : for U vy augment 31 line :

Finite differences Cumulative Integral

data Σ data 2 1 sys

x Y D x f : sol 005130 x Y D rkfixed : 21 sys

u sol 131 row 1 el : v sol 131 row 2 el : 21 mat 5 17021.1 21 mat

sol data Σ u v + 20 black 1 5 mat 3 1 sys

Simpson fails unexpectedly, why ?
X^Y [Power fnct] is NOT 'x' scalar 
thus rejected by the integrator . Σ U 1015 -^3 0.1 range : i 1 U rows range Cumul i el x f x U 1 el U i el int eval : for U Cumul augment 31 line :

above max ... NO meaning ! Σ #

f 05100 Int 17110.5

x y^y x ln * exp ≡

x^y = e^(y*ln(x))

ε 1015 -^:

x integral x ln x int maple : x 1 - x ln + (*

Σ U ε 5 0.5 range : i 1 U rows range Cumul i el x ln x U 1 el U i el int eval : for U Cumul augment 31 line :

Ln Σ o 5 blue plot :

setacc 1000 ≡

Ln x integral 2 1 sys