       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>

```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

```

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