Re: Bug of Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg82772] Re: Bug of Integrate*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Tue, 30 Oct 2007 05:47:46 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <fg4dfv$6c3$1@smc.vnet.net> <fg6pse$d44$1@smc.vnet.net>

David W.Cantrell wrote: <snip> > However, related to the above, version 5.2 does give an incorrect result > for a definite integral with a symbolic real limit. Whether this error > still exists in version 6, I don't know: > > In[3]:= Assuming[Element[x,Reals],Integrate[3*Sign[Cos[t]],{t,0,x}]] > > Out[3]= 3 If[x > 0, x Abs[Cos[x]] Sec[x], > Integrate[Sign[Cos[t]], {t, 0, x}, Assumptions -> x <= 0]] > > The above is incorrect for x > Pi/2. A correct result would have been > > 3 Sign[Cos[x]] (x - Pi Floor[x/Pi + 1/2]) > > for all real x. Hi David, Things have improved in version 6.0.1. In[1]:= Assuming[Element[x, Reals], Integrate[3*Sign[Cos[t]], {t, 0, x}]] Out[1]= 3 If[-(\[Pi]/2) <= x <= \[Pi]/2, x, Integrate[x Sign[Cos[t x]], {t, 0, 1}, Assumptions -> x \[Element] Reals && ! -(\[Pi]/2) <= x <= \[Pi]/2]] In[2]:= $Version Out[2]= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)" Best regards, -- Jean-Marc