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

1,2

Links

Table of n, a(n) for n=1..86.

Formula

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

Example

arclength = 1.311442498215547045545494653761965117948990...

Mathematica

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

Crossrefs

Cf. A333202, A334843.

Sequence in context: A171145 A271644 A262191 * A296457 A124020 A124234

Adjacent sequences: A334841 A334842 A334843 * A334845 A334846 A334847

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jun 15 2020

Status

approved