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A332629
Decimal expansion of arclength between (0,1) and (1,e) on y = e^x.
2
2, 0, 0, 3, 4, 9, 7, 1, 1, 1, 6, 2, 7, 3, 5, 2, 4, 7, 8, 5, 6, 9, 9, 0, 2, 7, 5, 2, 4, 2, 0, 2, 3, 9, 1, 3, 0, 8, 2, 1, 1, 4, 2, 7, 9, 5, 2, 3, 2, 0, 9, 4, 2, 1, 7, 9, 9, 9, 7, 0, 5, 2, 7, 2, 2, 8, 7, 7, 3, 9, 1, 5, 3, 7, 8, 9, 9, 7, 1, 5, 0, 7, 6, 0, 7
OFFSET
1,1
FORMULA
arclength = sqrt(1 + e^2) - sqrt(2) + arctanh(sqrt(2)) - arctanh(sqrt(1+e^2)).
EXAMPLE
arclength = 2.003497111627352478569902752420239130821142795232094...
MATHEMATICA
s = Integrate[Sqrt[1 + E^(2 x)], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Jun 12 2020
STATUS
approved