A334844 Decimal expansion of arclength between (0,0) and (1,sin 1) on y = sin x.

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

Offset: 1

Author

Clark Kimberling, Jun 15 2020

Keywords

• nonn
• cons
• easy

Examples

			arclength = 1.311442498215547045545494653761965117948990...
		

Crossrefs

Cf. A333202, A334843.

Programs

Mathematica

s = Integrate[Sqrt[1 + D[Sin[x], x]^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

Formula

arclength = sqrt(2)*E(1,1/2), where E = elliptic integral of the second kind.