A332631 Decimal expansion of arclength between (0,1) and (1,1/e) on y = 1/e^x.

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

Offset: 1

Author

Clark Kimberling, Jun 12 2020

Keywords

• nonn
• cons
• easy

Examples

			arclength = 1.192701401972154592777794219819503064418488768866...
		

Crossrefs

Cf. A333202, A332629.

Programs

Mathematica

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

Formula

arclength = sqrt(2) = sqrt(1+ 1/e^2) + arcsinh(e) - arcsinh(1).