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MathGroup Archive 2004

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Re: Fundamental theorem problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49592] Re: Fundamental theorem problem
  • From: pnardon <pnardon at ulb.ac.be>
  • Date: Sat, 24 Jul 2004 03:47:22 -0400 (EDT)
  • References: <cdqqnb$km6$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Steven Jonak 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!
> 
> S Jonak
> "Maintain an even strain."
> 
Try this

Simplify[D[Integrate[
     Sec[t], {t, 1, x^4}, Assumptions -> {Im[x] == 0, x > 1, x^4 < 
Ï?/2}], x]]


in fact it is usual that you need some assumptions to integrate from 1 
to x you need to say that x is real (first) then other specification...
that's math life


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