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Re: Correction to "Fundamental Theorem of Calculus and Mathematica"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100750] Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 13 Jun 2009 06:01:03 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <h0sbtl$hdk$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

this is nonsens.

f[x_] := Integrate[Sin[t^2], {t, 0, x}]
g[x_] := Integrate[Exp[-t^2], {t, 0, x}]

D[#, x] & /@ {g[x], f[x]}

gives

{E^(-x^2), Sin[x^2]}

That is why it is useful to post your full input and not a
verbal description.

Regards
   Jens

Len wrote:
> Greetings:
> 
> I define a function (using f[x_]:=) as the definite integral (from 0
> to x) of sin(t^2).  When I differentiate using Mathematica I get the
> correct answer of sin(x^2).
> 
> But when I define a function (using g[x_]:=) as the definite integral
> (from 0 to x) of e^(-t^2) and differentiate, I get the incorrect
> answer of 0.  (The correct answer is e^(-x^2).)
> 
> Why the inconsistency?
> 
> Oddly, if I define the function g above using "=" instead of ":=", all
> works well.
> 
> Can someone explain the odd behavior?
> 
> Thanks,
> 
> Len
> 


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