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MathGroup Archive 2004

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ArcCos[x] with x > 1

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49246] ArcCos[x] with x > 1
  • From: jaegerm at ibmt.fhg.de
  • Date: Fri, 9 Jul 2004 02:26:17 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

as the result of a definite integral (Integrate[r ArcCos[1/(2 r)] (1 +
4 r^2)^(1/2), {r, 1/2, 1/2^(1/2)}]) I received the expression
i*ArcCos[2]. How does Mathematica calculate ArcCos[x] with x > 1 which
is outside the function's domain [-1,1]? (Note, that I stay inside
this interval with the integration boundaries.) In Mathematica's
opinion, ArcCos[2] is a purely imaginary number, so why isn't
i*ArcCos[2] reduced to a real expession? How do I get an analytical
expression for the imaginary part of ArcCos[2]?

Magnus


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