A333203 Decimal expansion of arclength from (0,0) to (1,1) on y = x^3.

1, 5, 4, 7, 8, 6, 5, 6, 5, 4, 6, 8, 3, 6, 1, 0, 1, 4, 4, 7, 7, 5, 3, 3, 1, 6, 4, 6, 0, 6, 4, 2, 6, 0, 6, 1, 8, 0, 0, 6, 6, 3, 3, 3, 1, 7, 9, 4, 7, 0, 7, 2, 2, 5, 1, 3, 6, 8, 5, 9, 3, 9, 1, 6, 5, 5, 0, 2, 1, 1, 1, 4, 1, 2, 3, 2, 6, 0, 0, 7, 2, 6, 6, 9, 3, 1

Offset: 1

Author

Clark Kimberling, Jun 12 2020

Keywords

• nonn
• cons
• easy

Examples

			arclength = 1.54786565468361014477533164606426061800663...
		

Crossrefs

Cf. A333202, A333204.

Programs

Mathematica

s = Integrate[Sqrt[1 + 9 x^4], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

PARI

intnum(x=0, 1, sqrt(1+9*x^4)) \\ Michel Marcus, Jun 12 2020

Formula

arclength = 2F1(-1/2;1/4;5/4;-9), where 2F1 is the hypergeometric function.