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

**References**:**Correction to "Fundamental Theorem of Calculus and Mathematica"***From:*Len <lwapner2@gmail.com>