03493571-53ad-427b-bcaf-c9e44fdeba00 16 15 12 decimal

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

1. the function
2. user parameters a n x f a x n^* : a 1 : n 2 : 13 mat 21 sys

arc length of the parabola u arc 1 a n u f u diff (2^+ sqrt u int maple :

Accelerate the visit: integral accuracy => 50

a n x f x arc 2 1 sys

arc length of parabola [known] u arc 2 u * 14 u 2^* + sqrt * 2 u * asinh + 4 /

arc length of cubic => NOT so simple u cubic 1 a 3 u f u diff (2^+ sqrt u int :

u cubic maple u 19 u 4^* + (* 6 sqrt * 1 i + (* 413 i * u 2^* - sqrt * 13 i * u 2^* + sqrt * u 6 sqrt * 1 i + (* 2 / i EllipticF * + 36 sqrt * 1 i + (* 19 u 4^* + sqrt * /

1. assign arc length integrator as function
2. plot/calculate arc length cubic x arc_Cubic 1 a 3 u f u diff (2^+ sqrt u 0 x int eval :

more from scalar arc length integrator x Φ x arc_Cubic x arc / 1 - :

x g 0 :

x Φ x g - 0 ≡ x 1 - 1 solve 0.909 - 0.909 21 mat

x arc_Cubic x Φ

Arc_meter 9.87654321 :

meter 1 :

cumulative integration [unary arc length] Arc u 1 - 1 0.9 - range : i 1 u rows range Σ i el 1 a 3 x f x diff (2^+ sqrt x u 1 el u i el int : for u Σ augment 31 line :

Arc 1 10 1 1 - 2 2 mat 2 1 sys

Unary arc length 1 a 3 x f x diff (2^+ sqrt x 1 - 1 int 3.095731

User arc length 1 a 3 x f x diff (2^+ sqrt x 1 - 1 int Arc_meter * meter 30.575124