Re: Problem with definite integrals having symbolic limits

*To*: mathgroup at smc.vnet.net*Subject*: [mg21853] Re: [mg21850] Problem with definite integrals having symbolic limits*From*: Bojan Bistrovic <bojanb at physics.odu.edu>*Date*: Wed, 2 Feb 2000 22:54:13 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

> Dear MathGroup, > > I discovered what I think is an inconsistency and would like to check my > opinion and offer a suggestion to Wolfram. > When you do a "definite" integration with symbolic limits (instead of > concrete numbers), the result you get may not be unconditionally true. The > necessary conditions are not stated by Mathematica, although > "GenerateConditions" is set to True. > > The notebook added demonstrates this problem. I suggest that a warning > message should be given, that describes the conditions for the stated > result. > > With best regards, > Wolter Kaper > dept. of Chemistry > Univ. of Amsterdam > The "problem" is the folowing: you use Set to define you function instead of SetDelayed: In[1]:= Int[xend_] = Integrate[1/x^2, {x, -2, xend}, GenerateConditions -> True] The right hand side is evaluated AT THIS TIME, so, since "xend" is just a symbol, the result is calculated and assigned to your function: Out[1]= -1/2 - 1/xend In[2]:= ?Int Out[2]= Global`Int Int[xend_] = -1/2 - xend^(-1) So when you type Int[2], you get the wrong result. What you should do is In[3]:= Int[xend_] := Integrate[1/x^2, {x, -2, xend}, GenerateConditions -> True] In[4]:= ?Int Out[4]= Global`Int Int[xend_] := Integrate[1/x^2, {x, -2, xend}, GenerateConditions -> True] In[5]:= Int[2] Out[5]= Infinity Now, SHOULD the integrate return the result like: If[xend > -2 && xend < 0, -(2 + xend)/(2*xend), Integrate[a/x^2, {x, -2, xend}]] Well, if you try Integrate[a/x^2, {x, -2, xend}, GenerateConditions -> True, Assumptions->{a>0}] you get If[xend > -2 && xend < 0, -(a*(2 + xend))/(2*xend), Integrate[a/x^2, {x, -2, xend}]] It looks bizzare :-). SetDelayed will solve your problem for the time, and as for the question about inconsistency, it looks like one to me. Bye, Bojan -- ------------------------------------------------------------- Bojan Bistrovic, bojanb at physics.odu.edu Old Dominion University, Physics Department, Norfolk, VA -------------------------------------------------------------