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Re: Bug of Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82770] Re: Bug of Integrate
  • From: Thomas E Burton <tburton at brahea.com>
  • Date: Tue, 30 Oct 2007 05:46:44 -0500 (EST)

Sort of a bug, more of a misunderstanding. The argument has two  
roots, +/-3. You took one value; version 6.0.1 took another. Version  
5 takes a mixture of the two roots, apparently, and yields 0. Both  
versions yield

3*t*Cos[t]*Sqrt[Sec[t]^2]

for the indefinite integral; that is, neither version hazards a guess  
as to which sign of the square root you want. The "bug" occurs when  
you ask for various definite integrals. Versions 5 and 6 differ from  
each other and also vary by what limits you choose. For instance, if  
you integrate from 0 to Pi/2, version 6 chooses the positive root,  
and if you integrate from 0 to Pi, you get zero! Given the ambiguity  
of the integrand, none of these answers are wrong, exactly. Beware.

> 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.



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