<p> hatch region </p>

625147d3-7c8d-4396-9800-56df7a104108 23 3 5 decimal

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

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

Simpson Integrator in the Transformed Domain [0,1] <= [a,b]

The Smath "normalised" integrator companion ... enables integration of the 'ainterp, cinterp' 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 / : 13 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 * 51 line :

sanity check the sextuplets Mathcad 11 Adaptiv 5.40752818465632 ≡ Technical accuracy 5.40752818465627 ≡ Simpson Transf'd.. 5.40752818465635 ≡ Smath Simpson 7½ D 5.4075281 ≡ Simplex 10½ D .... 5.40752818462 ≡ MCD Romberg TOL -7 5.40752809219025 ≡ 61 line

x f x sqrt exp :

x g 0 :

transformed domain [0,1] <= Simpson [a,b] f 0210000 Int 5.40752818465635

region x f x g 0210 hatch :

x f

The naive test fnct to integrate

x f region 2 1 sys

f a b n Simpson h b a - n / : 13 / h 2 / a f b f + (* h a k h * + f k 1 n 1 - sum * + (* 23 / h * a h 2 / - k h * + f k 1 n sum * + eval 21 line :

Most remarkable Simpson Transformed Domain !

x f 1 x - ln - x / :

TOL 1012 -^:

Zeta(2) => 1.644934066848226

x f 1 10 1 1 - 2 2 mat 2 1 sys

f TOL 1 TOL - (10000 Int 1.644934065

x f x TOL 1 TOL - (int 1.645187342