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. ZAE Weiergewan 11, rue Edmond Reuter L-5326 Contern Luxembourg Phone: +352 2454 2566 Fax: +352 2454 3566 Website: www.iee.lu This e-mail may contain trade secrets or privileged, undisclosed or otherwise confidential information. If you are not the intended recipient and have received this e-mail in error, you are hereby notified that any review, copying or distribution of it is strictly prohibited. Please inform us immediately and destroy the original transmittal from your system. Thank you for your co-operation.