Re: Bug of Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg82727] Re: [mg82708] Bug of Integrate
- From: DrMajorBob <drmajorbob at bigfoot.com>
- Date: Tue, 30 Oct 2007 03:21:59 -0500 (EST)
- References: <487369.1193679105223.JavaMail.root@m35>
- Reply-to: drmajorbob at bigfoot.com
Actually, the correct answer is 0.
Integrate[Sqrt[1/Cos[t]^2]*3*Cos[t],{t,0,2Pi}]
-6 \[Pi]
Plot[Sqrt[1/Cos[t]^2]*3*Cos[t],{t,0,2Pi}]
Quiet@NIntegrate[Sqrt[1/Cos[t]^2]*3*Cos[t],{t,0,2Pi}]
-3.55271*10^-15
Plot[3 Sign@Cos[t] - Sqrt[1/Cos[t]^2]*3*Cos[t], {t, 0, 2 Pi},
PlotRange -> All]
Integrate[3 Sign@Cos[t],{t,0,2Pi}]
0
Either way, Integrate got it wrong. But so did you:
> Simplifying the expresion resultrs Integrate[3,{t,0,2*Pi}]
No.
Sqrt[1/Cos[t]^2]*3*Cos[t] // FullSimplify
3 Cos[t] Sqrt[Sec[t]^2]
Integrate[Sqrt[1/Cos[t]^2]*3*Cos[t] // FullSimplify, {t, 0, 2 Pi}]
-6 \[Pi]
Bobby
On Mon, 29 Oct 2007 05:35:57 -0500, Miguel <misvrne at gmail.com> 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.
>
> Simplifying the expresion resultrs Integrate[3,{t,0,2*Pi}] and It is
> clear that the correct solution is 6*Pi.
>
> Is a bug of Version 6.0.1?
>
>
>
--
DrMajorBob at bigfoot.com