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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[1]:= g[x_] := Integrate[E^(-t^2), {t, 0, x}]
In[2]:= g'[x]
Out[2]= 0
In[3]:= D[g[x], x]
Out[3]= 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
> 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 ":=", al=
l
> works well.
>
> Can someone explain the odd behavior?
>
> Thanks,
>
> Len
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