A332629 Decimal expansion of arclength between (0,1) and (1,e) on y = e^x.
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
Examples
arclength = 2.003497111627352478569902752420239130821142795232094...
Programs
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Mathematica
s = Integrate[Sqrt[1 + E^(2 x)], {x, 0, 1}] r = N[s, 200] RealDigits[r][[1]]
Formula
arclength = sqrt(1 + e^2) - sqrt(2) + arctanh(sqrt(2)) - arctanh(sqrt(1+e^2)).