<p> Singular(f,a,b,TOL) </p>

a803d954-b794-47c0-afba-a9506ad996fc 14 4 5 decimal

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

x ln

True value => -1
integral accuracy 10000 x ln x 1099 -^1 int 1.0036 -

relative error 1 1.0036 - 1 - / - 0.0036 -

Work sheet option: integral accuracy 10000

<p> Singular(f,a,b,TOL) </p>

Simgular end point Smath  TOL adaptive integration f a b TOL Singular Y1 b a - (a b + 2 / f * : Y2 b a - 6 / 2 a * b + 3 / f a 2 b * + 3 / f + (* : N 2 : Y1 Y2 - abs TOL ≥ Y1 Y2 : N 2 N * : Y2 0 : h b a - N / : j 2 N range x0 a j 1 - (h * + : x1 x0 h + : Y2 Y2 h x0 f x1 f + 2 / (* + : 31 line for 51 line while Y2 51 line eval :

a 1099 -^: b 0.1 : c 0.25 : 13 mat

x f x ln :

a f 227.9559 -

x f b 1 b 10 - 2 2 mat c 1 c 10 - 2 2 mat 3 1 sys

t0 1 time :

set higher TOL on the steep subspace ∫1 f a b 0.00001 Singular : 0.3303 -

1 time t0 - min 24.6

∫2 f b c 0.0001 Singular : 0.2662 -

Integral accuracy 10000 ∫3 x f x c 1 int : 0.4034 -

Σ ∫1 ∫2 + ∫3 + : 0.99991 -

relative error 1 Σ 1 - / - 0.0001

x f 11 x + / :

x f x f x diff 2 1 sys

ALL true digits each
Not singular endpoint. x f x 010 int x f x diff x 010 int 21 mat 2.39789527279838 0.909090909090909 - 21 mat