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