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Re: Re: Correction to "Fundamental Theorem of

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100757] Re: [mg100746] Re: [mg100727] Correction to "Fundamental Theorem of
  • From: Mauricio Esteban Cuak <cuak2000 at gmail.com>
  • Date: Sat, 13 Jun 2009 06:02:20 -0400 (EDT)
  • References: <200906120946.FAA27917@smc.vnet.net>

It works on my version too (Mathematica 6 for OS X, 32 bit)

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

D[g[x], x]


Out[9]:= E^(-x^2)


2009/6/12 Bob Hanlon <hanlonr at cox.net>

> Works in my version.
>
> $Version
>
> 7.0 for Mac OS X x86 (64-bit) (February 19, 2009)
>
> f[x_] := Integrate[Sin[t^2], {t, 0, x}]
>
> D[f[x], x]
>
> Sin[x^2]
>
> g[x_] := Integrate[Exp[-t^2], {t, 0, x}]
>
> D[g[x], x]
>
> E^(-x^2)
>
>
> Bob Hanlon
>
> ---- Len <lwapner2 at gmail.com> 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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