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MathGroup Archive 2004

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Re: Fundamental theorem problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49583] Re: Fundamental theorem problem
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Sat, 24 Jul 2004 03:47:13 -0400 (EDT)
  • References: <cdqqnb$km6$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Steven Jonak" <jonakst at gw.kirkwood.k12.mo.us> wrote:
> 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!

Consider

In[1]:= Assuming[x^4 < Pi/2, Simplify[D[Integrate[Sec[t], {t, 1, x^4}], x]]]

Out[1]= 4*x^3*Sec[x^4]

HTH,
David Cantrell


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