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Re: Integral wit Norm function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88293] Re: [mg88271] Integral wit Norm function
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 1 May 2008 03:18:45 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

alfa[t_] := {t^2, 4 t, 8 t^3}

normt[t_] = Simplify[Norm[alfa[t]], t > 0]

t*Sqrt[64*t^4 + t^2 + 16]

Clear[int];

int[a_] = 
 FullSimplify[Integrate[normt[t], {t, 1, a}, Assumptions -> {a > 0}]]

(1/8192)*(16*Sqrt[64*a^4 + a^2 + 
            16]*(128*a^2 + 1) + 
      4095*ArcSinh[(128*a^2 + 1)/
            (3*Sqrt[455])] - 
      (9/2)*(4128 + 455*Log[91/5]))

Plot[int[a], {a, 0, 2}]


Bob Hanlon

---- Miguel <misvrne at gmail.com> 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.
> 
> Thanks
> 



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