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Re: Integral wit Norm function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88286] Re: Integral wit Norm function
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 30 Apr 2008 07:03:00 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fv9adn$mqd$1@smc.vnet.net>

Miguel wrote:

> How can I to calculate the integral of an expression which include
> Norm function?. By example,
> 
> Let the curve  alfa[t_]:={t^2,4t, 8t^3}. Calculate
> Integral[Norm[alfa[t]],{t,1,a}], where a is Real and >0.

Using the right command, i.e. *Integrate* rather than Integral (which 
does not exist in Mathematica), with some options such as *Assumptions* 
should help greatly.

alfa[t_] := {t^2, 4 t, 8 t^3}
Integrate[Norm[alfa[t]], {t, 1, a},
  Assumptions -> Element[a, Reals] && a > 0]

\[Piecewise] {
   {(1/16384)(-37152 + 32 Sqrt[16 + a^2 + 64 a^4] +
      4096 a^2 Sqrt[16 + a^2 + 64 a^4] +
      8190 ArcSinh[(1 + 128 a^2)/(3 Sqrt[455])] - 4095 Log[91/5]),
    a > 1 || 0 < a < 1}
  }

Regards,
-- Jean-Marc



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