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Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
*To*: mathgroup at smc.vnet.net
*Subject*: [mg100773] Re: Correction to "Fundamental Theorem of Calculus and Mathematica"
*From*: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
*Date*: Sat, 13 Jun 2009 06:05:15 -0400 (EDT)
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 ":=", all
works well.
Can someone explain the odd behavior?
Thanks,
Len
Hi, Len,
I tried and this is the result:
In[3]:= g[x_] := Integrate[Exp[-t^2], {t, 0, x}]
In[4]:= D[g[x], x]
Out[4]= \[ExponentialE]^-x^2
Sorry, Alexei
--
Alexei Boulbitch, Dr., habil.
Senior Scientist
IEE S.A.
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