Re: Bug of Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg82731] Re: Bug of Integrate
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Tue, 30 Oct 2007 03:24:02 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <fg4dfv$6c3$1@smc.vnet.net>
Miguel wrote:
> When I try to calculate the integral
>
> Integrate[Sqrt[1/Cos[t]^2]*3*Cos[t],{t,0,2Pi}] Mathematica 6.0.1
> yields -6*Pi.
Mathematica 5.2 and 6.0.1 disagree here, though the result returned by
5.2 is correct.
In[1]:=
$Version
Out[1]=
5.2 for Microsoft Windows (June 20, 2005)
In[2]:=
Integrate[Sqrt[1/Cos[t]^2]*3*Cos[t],{t,0,2Pi}]
Out[2]=
0
In[1]:= $Version
Out[1]= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)"
In[2]:= Integrate[Sqrt[1/Cos[t]^2]*3*Cos[t], {t, 0, 2 Pi}]
Out[2]= -6 \[Pi]
> Simplifying the expresion resultrs Integrate[3,{t,0,2*Pi}] and It is
> clear that the correct solution is 6*Pi.
Erroneous simplification on the interval [0, 2Pi): this is valid only
for t between 0 and Pi/2 and t between 3Pi/2 and 2Pi (otherwise the
cosine is negative). The correct simplification is as below:
In[1]:= Simplify[Sqrt[1/Cos[t]^2]*3*Cos[t],
Assumptions -> 0 <= t < 2*Pi]
Out[1]= 3 Abs[Sec[t]] Cos[t]
> Is a bug of Version 6.0.1?
It looks like that neither Mathematica 6.0.1 nor you were correct :-)
The correct result, zero, is returned by version 5.2.
In[3]:= Plot[Sqrt[1/Cos[t]^2]*3*Cos[t], {t, 0, 2 Pi}]
In[4]:= Integrate[3 Abs[Sec[t]] Cos[t], {t, 0, 2 Pi}]
Out[4]= 0
Regards,
--
Jean-Marc