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Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
*To*: mathgroup at smc.vnet.net
*Subject*: [mg100795] Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
*From*: Albert Retey <awnl at gmx-topmail.de>
*Date*: Sun, 14 Jun 2009 05:39:54 -0400 (EDT)
*References*: <h0sbtl$hdk$1@smc.vnet.net> <h0t856$r80$1@smc.vnet.net> <h0vtok$79n$1@smc.vnet.net>
Hi,
> Interesting! Like you, I get correct results when differentiating
> using "D". But when I differentiate using the prime sign (g'[x] ) I
> get the incorrect answer of 0.
I think this is a case where Trace is useful, and when looking at the
output of Trace it seems clear that this is why it goes wrong for g':
In[14]:= Integrate[Exp[-t^2], {t, 0, #}]
Out[14]= 1/2 Sqrt[\[Pi]] Erf[3]
In[15]:= Integrate[Sin[t], {t, 0, #}]
Out[15]= 1 - Cos[#1]
I think Out[14] clearly is a bug, because whatever # may be, it is not 3
in almost all cases :-)
hth,
albert
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