Integrate question

*To*: mathgroup at smc.vnet.net*Subject*: [mg77600] Integrate question*From*: dimitris <dimmechan at yahoo.com>*Date*: Wed, 13 Jun 2007 07:44:47 -0400 (EDT)

This question aose after replying in the forum for another CAS. In fact, it is not a question on "how I do something" but rather asking about some information about "why". In view of my reply I realized one fundamental difference between Integrate and the function Int from another CAS. int( diff(y(x),x) , x=a..b); b / | d | -- y(x) dx | dx / a In[11]:= Integrate[Derivative[1][f][x], {x, a, b}] Out[11]= -f[a]+f[b] I guess all we are familiar with the first fundamental theorem of calculus. It holds (http://mathworld.wolfram.com/ FundamentalTheoremsofCalculus.html) if the function f[x] is continuous on the closed interval [a,b] (or at least piecewise continuous in Newton-Leibniz form with limits left and right of the finite discontinuities). I am with Mathematica default design. For example In[12]:= Integrate[Derivative[1][f][x]*Derivative[2][f][x], {x, a, b}] Out[12]= (1/2)*(-Derivative[1][f][a]^2 + Derivative[1][f][b]^2) In[13]:= Integrate[Derivative[1][f][x]*g[x] + f[x]*Derivative[1][g][x], {x, a, b}] Out[13]= (-f[a])*g[a] + f[b]*g[b] In[14]:= Integrate[Sin[f[x]]*Derivative[1][f][x], {x, a, b}] Out[14]= Cos[f[a]] - Cos[f[b]] I am neither software enginner, nor pure mathematician but this fundmental difference impressed me a lot! I am familiar with the issue of generic complex values in mathematica but here Mathematica "assumes" that typing Integrate[f'[x],{x,a,b}] f[x] is continuous in [a,b]? I will appreciate any comments on this issue. Greeting from the sunny Athens, Dimitris

**Follow-Ups**:**Re: Integrate question***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>