       Re: Correction to "Fundamental Theorem of Calculus and

• To: mathgroup at smc.vnet.net
• Subject: [mg100754] Re: Correction to "Fundamental Theorem of Calculus and
• From: Len <lwapner2 at gmail.com>
• Date: Sat, 13 Jun 2009 06:01:47 -0400 (EDT)
• References: <h0t84r\$r7k\$1@smc.vnet.net>

```Hi Bob:

For some reason Mathematica doesn't like the "prime notation".  (See
below).  The prime notation does work for the
sin (t^2) example.  Do you know why this is the case?

Thanks -

Len

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

In:= g'[x]

Out= 0

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

Out= E^-x^2

On Jun 12, 2:46 am, Bob Hanlon <hanl... at cox.net> wrote:
> 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 <lwapn... 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
>
> 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 ":=", al=
l
> works well.
>
> Can someone explain the odd behavior?
>
> Thanks,
>
> Len

```

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