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Integrating Abs[Sin[]^2]

• To: mathgroup at smc.vnet.net
• Subject: [mg38830] Integrating Abs[Sin[]^2]
• From: Jos R Bergervoet <antispam at nospam.com>
• Date: Wed, 15 Jan 2003 02:19:39 -0500 (EST)
• Organization: Philips Research Laboratories
• Sender: owner-wri-mathgroup at wolfram.com

A strange result appeared when using

    Mathematica 4.1 for Linux
    Copyright 1988-2000 Wolfram Research, Inc.
     -- Motif graphics initialized --

in computing the following:

  result = Integrate[ Abs[Sin[k x]]^2, {x,0,1}]
  N[ result /. k->I+1 ]

(*  Analytical approach gives 0.261044 + 0.616283 I,  WRONG !!! *)

  k=I+1; NIntegrate[ Abs[Sin[k x]^2], {x,0,1}]

(*  Numerical check gives 0.679391  *)


So why is the analytical result for |Sin[k x]|^2 wrong?
What should I do to circumvent such errors?

Thanks in adv.,

-- Jos  <jos.bergervoet at philips.no_s_p_a_m.com>

PS: For those interested, the correct analytical result is:

         (Sinh[2Im[k]]/Im[k] - Sin[2Re[k]]/Re[k]) / 4

• Follow-Ups:
  • Re: Integrating Abs[Sin[]^2]
    • From: Dr Bob <majort@cox-internet.com>