262c02d8-db25-47ae-a8a4-bfa27506936d 26 6 12 decimal

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

Indefinite Integral

β 4.69292878185 2.485645088668 0.005049502793 - 0.008399478307 - 5.19337552684 0.698811411628 0.043875966805 - 0.000673223801 - 81 mat :

appVersion 0.98.6179 ≡ Timing 1.5 min ≡ 21 mat

x f x x β 3 el x * β 2 el + β 4 el x 2^* + (* β 1 el + (* 1 x x β 7 el x * β 6 el + β 8 el x 2^* + (* β 5 el + (* + / : x Deriv x f (x diff : 21 line

This session is Edu. for future Engineering works. It has nothing to do with accuracy of integration as based on the native ∫ Simpson [acc 100].

u Q x f : z ∫ u Q u 0 x int : x ∫ z ∫ : 31 line

x c 10 x ≤ (x 15 ≤ (& cases :

recast integ'r

t0 1 time :

Smath plot span => 164 pixels Integrator runs 164 times

0 x ≤ ( x 15 ≤ ( & x ∫ not sanity fit if 15 64 15 32 2 2 mat 2 1 sys

1 time t0 - 2.5 s *

t0 1 time :

x f x c * x Deriv x c * 2 1 sys

1 time t0 - 0.7 s *

faster > ∫(x)*c(x) 
... 2.9/4.2 0 x ≤ (x 15 ≤ (& x ∫ not sanity fit if

The Gaussian b-spline

x c 12 - x ≤ (x 2 ≤ (& cases :

u b 0 u 2 - ≤ 16 / 2 u + (3^* 2 - u ≤ (u 1 - ≤ (& 16 / 2 u + (3^* 23 / 1 u + (3^* - 1 - u ≤ (u 0 ≤ (& 23 / 1 u - (3^* - 16 / 2 u - (3^* + 0 u ≤ (u 1 ≤ (& 16 / 2 u - (3^* 1 u ≤ (u 2 ≤ (& 0 cases :

z indefinite u b u x - x int :

t0 1 time :

x b x c * x indefinite x c * 2 1 sys

1 time t0 - 36 s *

exact acc 100
exact by design x b x 2 - 2 int 1.000000000000000

Scalar has two meaning ... 1.23456789 is a scalar number, π ...etc 'x' in b(x), indefinite(x) is scalar, i.e: 'x' is a vanishing iterator. As 'x' runs in the X Cartesian direction, at each canvas pixel the Cartesian Y's are evaluated and plotted. The plots reside in the WS as long as active. They vanish as the Work Sheet is closed. [-2 ..2] is 222 pixels thus calculate b(x), indefinite(x) 222 * each

Recast . . . recast what ?

Smath is both styles: scalar wrt plot and wrt most solvers.

Under the hood, Smath is as well vector style, so gorgeous

for stored evaluated stuff from previous session(s).

At this point in our session, the integrator is consumed

from the front end f(x) . . . thus must be re-assigned ,

like paired with a new executable session Φ(x).

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z single u Φ u 0 x int :

exponent positive
integer/fractional x Φ x 2^:

transit x single z single :

x Φ x single 2 1 sys

user X 1 :

X Φ X single 21 mat 1 0.333333 21 mat

z multiple x Φ u Φ u 0 x int u Φ u 0 x int u 0 x int u Φ u 0 x int u 0 x int u 0 x int 41 sys :

x multiple

x multiple z multiple :

X 2 :

X multiple 4 2.666667 5.333333 10.666667 41 sys

x multiple 1 1 3 / + 20 black 1 5 mat 2 1 sys

x f x 0.5 1 -^x - exp * :

x f x int π sqrt x sqrt erf * ≡

x 0.1 :

http://www.wolframalpha.com/input/?i= integrate+x%5E(0.5-1)*exp(-x)+from+0+to+0.1

π sqrt x sqrt erf * 0.61199136611177

x f π sqrt x sqrt erf * 2 1 sys

x 0.1 :

x Gamma π sqrt x sqrt erf * 21 mat 9.5135 0.612 21 mat

π sqrt x sqrt erf * 0.611991