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

```

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