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

• To: mathgroup at smc.vnet.net
• Subject: [mg100767] Re: [mg100727] Correction to "Fundamental Theorem of Calculus and Mathematica"
• From: Curtis Osterhoudt <cfo at lanl.gov>
• Date: Sat, 13 Jun 2009 06:04:10 -0400 (EDT)
• Organization: LANL
• References: <200906120144.VAA17857@smc.vnet.net>

```  Works here ("7.0 for Linux x86 (32-bit) (November 11, 2008)").

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

In:= D[f[x], x]

Out= Sin[x^2]

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

In:= D[g[x], x]

Out= E^-x^2

On Thursday 11 June 2009 07:44:34 pm 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
>
> 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
>
> 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
>
>

--
==================================
Curtis Osterhoudt
cfo at remove_this.lanl.and_this.gov
PGP Key ID: 0x4DCA2A10
==================================

```

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