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

2f861c48-9490-46e7-b7fa-473ecec3bd93 14 4 5 decimal

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

Major Radius a 0.5 :

Minor Radius b 1 :

Ellipse Eccentricity ε 1 b 2^a 2^/ - sqrt :

http://paulbourke.net/geometry/ellipsecirc/

t0 1 time :

Perimeter of an  [a, b] Ellipse
... acc 10000 ≡ acc 100 P 4 a * 1 ε 2^θ sin (2^* - sqrt θ 0 π 2 / int * : 4.84422411027386

1 time t0 - 28.9 s *

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

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 
Integration accuracy from user command line 'n' f a b n ∫ 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 :

f a b n ∫

x λ 10 x ≤ (x π 2 / ≤ (& cases :

x f 1 ε 2^x sin (2^* - sqrt :

t0 1 time :

Gains timing @ high acc  ... try/compare acc 10000
set ... ∫(f,0,π/2,200) Perim 4 a * f 0 π 2 / 200 ∫ * : 4.84422411027384

1 time t0 - 1 s *

x f x λ *

x q x sqrt :

t0 1 time :

Does not converge @ acc 10000 Ω x q x 0100 int : 666.666637963573

1 time t0 - 11 s *

t0 1 time :

x f x q :

perfectly convergent f 01002000 ∫ 666.666666666669

1 time t0 - 8 s *

4.44444444444444 105^* sqrt 666.666666666666