bb70d32c-34f2-4cad-bffd-37ee9a7cb83e 15 3 5 decimal

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

t f 0 t π 2 / ≤ 0 t π ≥ (t 3 π * 2 / ≤ (& t sin cases :

x f

integral accuracy 10000 x Int u f u 0 x int :

1 π * Int 1.00523598809422

4 Int 1.00408313811726

3 appVersion 0.98.6179 ≡

Explain: if/else is not scalar wrt the integrand Φ(u) ... if/otherwise is scalar wrt f(u)

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t Φ t π 2 / ≤ 0 t π ≥ (t 3 π * 2 / ≤ (& 0 t sin if if :

x Φ

x Σ u Φ vectorize u 1012 -^x int :

4 Σ #

f a b Int x f x a b int 32 / b a - (* w G w 01 int * ≡ memo ≡ w s b a - (34 / 2 w * 1 - (* 14 / 2 w * 1 - (3^* - 12 / + (* a + : w G w s f 12 w * 1 - (2^- (* : 32 / b a - (* w G w 01 int * 41 line :

Inaccurate from native Simpson
set option integral acc 10000 Φ 04 Int 0.997887257501154

Fnct x 03 π * (0.05 range : i 1 x rows range u i el x i el : Fnct i el u i el Φ eval : 21 line for u Fnct augment 31 line :

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 * (* + eval : 21 line for vx Y augment 61 line :

Fnct 1 1 sys

Discontinuous functions must be specified completely. The Smath numerical integrator does not take disconti- nuous if/else, thus: use the finite differences integrator.

Finite differences Cumulative Integral

Fnct Σ Fnct 2 1 sys