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Decimal expansion of arclength between (0,1) and (1,e) on y = e^x.
2

%I #12 Jul 06 2020 21:36:56

%S 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,

%T 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,

%U 3,9,1,5,3,7,8,9,9,7,1,5,0,7,6,0,7

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

%F arclength = sqrt(1 + e^2) - sqrt(2) + arctanh(sqrt(2)) - arctanh(sqrt(1+e^2)).

%e arclength = 2.003497111627352478569902752420239130821142795232094...

%t s = Integrate[Sqrt[1 + E^(2 x)], {x, 0, 1}]

%t r = N[s, 200]

%t RealDigits[r][[1]]

%Y Cf. A333202, A332630, A332631.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Jun 12 2020