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A333202
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Decimal expansion of arclength from (0,0) to (1,1) on y = x^2.
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19
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1, 4, 7, 8, 9, 4, 2, 8, 5, 7, 5, 4, 4, 5, 9, 7, 4, 3, 3, 8, 2, 7, 9, 0, 6, 0, 1, 9, 4, 3, 3, 9, 1, 4, 4, 3, 5, 0, 7, 1, 6, 9, 7, 4, 3, 0, 5, 9, 5, 0, 0, 8, 2, 5, 1, 8, 8, 1, 2, 1, 2, 2, 4, 9, 3, 3, 5, 3, 8, 3, 3, 6, 3, 5, 2, 5, 0, 6, 8, 7, 8, 0, 5, 1, 6, 2
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OFFSET
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1,2
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LINKS
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FORMULA
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arclength = (2 sqrt(5) + arcsinh(2))/4.
arclength = (2 sqrt(5) + log(2 + sqrt(5)))/4.
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EXAMPLE
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Equals 1.478942857544597433827906...
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MATHEMATICA
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s = Integrate[Sqrt[1 + 4 x^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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