Re: Correction to "Fundamental Theorem of Calculus and

• To: mathgroup at smc.vnet.net
• Subject: [mg100802] Re: [mg100727] Correction to "Fundamental Theorem of Calculus and
• From: peter <plindsay.0 at gmail.com>
• Date: Sun, 14 Jun 2009 05:41:13 -0400 (EDT)
• References: <200906120144.VAA17857@smc.vnet.net>

```In[1]:= f[x_]:=Integrate[Sin[t^2],{t,0,x}]
In[2]:= D[f[x],x]
Out[2]= Sin[x^2]
In[3]:= g[x_]:=Integrate[Exp[-t^2],{t,0,x}]
In[4]:= D[g[x],x]
Out[4]= E^-x^2
In[9]:= \$Version
Out[9]= 7.0 for Mac OS X x86 (32-bit) (February 18, 2009)

2009/6/12 Len <lwapner2 at gmail.com>:
> 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
>
>

--
Peter Lindsay

```

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