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