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MathGroup Archive 2004

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Re: AW: Fundamental theorem problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49636] Re: [mg49581] AW: [mg49573] Fundamental theorem problem
  • From: DrBob <drbob at bigfoot.com>
  • Date: Sun, 25 Jul 2004 02:55:45 -0400 (EDT)
  • References: <200407240747.DAA05761@smc.vnet.net>
  • Reply-to: drbob at bigfoot.com
  • Sender: owner-wri-mathgroup at wolfram.com

FullSimplify has no success at my machine (version 5.0.1):

FullSimplify[D[Integrate[
     Sec[t], {t, 1, x^4}], x]]
4*x^3*If[(Re[x^4] < Pi ||
       Im[x^4] != 0) &&
      (Pi + x^4 == 0 ||
       Im[x^4] != 0 ||
       Pi + Re[x^4] > 0) &&
      (Pi + 2*x^4 == 0 ||
       Pi + 2*Re[x^4] > 0 ||
       Im[x^4] != 0) &&
      (2*x^4 == Pi ||
       2*Re[x^4] < Pi ||
       Im[x^4] != 0),
     -((1/(-1 + x^4))*
       (2*(ArcTanh[Tan[1/2]] -
         ArcTanh[Tan[x^4/
           2]]))), Integrate[
      Sec[1 + t*(-1 + x^4)],
      {t, 0, 1},
      Assumptions ->
        !((Re[x^4] < Pi ||
          Im[x^4] != 0) &&
         (2*x^4 == Pi ||
          2*Re[x^4] < Pi ||
          Im[x^4] != 0) &&
         (Pi + x^4 == 0 ||
          Im[x^4] != 0 ||
          Pi + Re[x^4] > 0) &&
         (Pi + 2*x^4 == 0 ||
          Pi + 2*Re[x^4] >
           0 || Im[x^4] !=
           0))]] + (-1 + x^4)*
    If[(Re[x^4] < Pi ||
       Im[x^4] != 0) &&
      (Pi + x^4 == 0 ||
       Im[x^4] != 0 ||
       Pi + Re[x^4] > 0) &&
      (Pi + 2*x^4 == 0 ||
       Pi + 2*Re[x^4] > 0 ||
       Im[x^4] != 0) &&
      (2*x^4 == Pi ||
       2*Re[x^4] < Pi ||
       Im[x^4] != 0),
     (8*x^3*(ArcTanh[
          Tan[1/2]] - ArcTanh[
          Tan[x^4/2]]))/
       (-1 + x^4)^2 +
      (4*x^3*Sec[x^4/2]^2)/
       ((-1 + x^4)*(1 -
         Tan[x^4/2]^2)),
     Integrate[(4*t*x^3)*
       Sec[1 + t*(-1 + x^4)]*
       Tan[1 + t*(-1 + x^4)],
      {t, 0, 1},
      Assumptions ->
        !((Re[x^4] < Pi ||
          Im[x^4] != 0) &&
         (2*x^4 == Pi ||
          2*Re[x^4] < Pi ||
          Im[x^4] != 0) &&
         (Pi + x^4 == 0 ||
          Im[x^4] != 0 ||
          Pi + Re[x^4] > 0) &&
         (Pi + 2*x^4 == 0 ||
          Pi + 2*Re[x^4] >
           0 || Im[x^4] !=
           0))]]

Bobby

On Sat, 24 Jul 2004 03:47:11 -0400 (EDT), <Matthias.Bode at oppenheim.de> wrote:

> Hello Steven,
>
> FullSimplify[D[Integrate[Sec[t],
>     {t, 1, x^4}], x]]
>
> yields:
>
> 4*x^3*Sec[x^4]
>
> Satisfied?
>
> Best regards,
> Matthias Bode
> Sal. Oppenheim jr. & Cie. KGaA
> Untermainanlage 1
> D-60329 Frankfurt am Main
> GERMANY
> Tel.: +49(0)69 71 34 53 80
> Mobile: +49(0)172 6 74 95 77
> Fax: +49(0)69 71 34 95 380
> E-mail: matthias.bode at oppenheim.de
> Internet: http://www.oppenheim.de
>
>
>
> -----Ursprüngliche Nachricht-----
> Von: Steven Jonak [mailto:jonakst at gw.kirkwood.k12.mo.us]
> Gesendet: Freitag, 23. Juli 2004 12:02
> An: mathgroup at smc.vnet.net
> Betreff: [mg49573] Fundamental theorem problem
>
>
> I input the command: D[Integrate[Sec[t],{t,1,x^4}],x] expecting to get
> 4x^3 Sec[x^4] but instead got a fairly complicated result that doesn't
> resemble what one would expect from the Fundamental Theorem of Calculus.
>  What am I doing wrong? Help!
>
> S Jonak
> "Maintain an even strain."
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net


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