Re: Antiderivatives and Definite Integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg39683] Re: [mg39670] Antiderivatives and Definite Integrals
• From: Dr Bob <drbob at bigfoot.com>
• Date: Sat, 1 Mar 2003 22:04:47 -0500 (EST)
• References: <200303010747.CAA09858@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```It's really just an example of getting the wrong general antiderivative
when x isn't specified, but the right integral when x *is* specified.

f[x_] = Integrate[Sqrt[1 + Cos[t]], {t, 0, x}]
g[x_] := Integrate[Sqrt[1 + Cos[t]], {t, 0, x}]
Plot[{Sqrt[1 + Cos@t], f@t, g@t}, {t, 0, 2Pi}]

Bobby

On Sat, 1 Mar 2003 02:47:47 -0500 (EST), Garry Helzer <gah at math.umd.edu>
wrote:

> The antiderivative of Sqrt[1+Cos[x]] discussed here recently (sorry, I
> lost the thread) provides an amusing illustration of the fact that
> Mathematica does not always evaluate definite integrals by first finding
> an antiderivative and then substituting in the upper and lower limits.
> (See the Mathematica book A.9.5) Make the definitions
>
> f[x_] = Integrate[Sqrt[1 + Cos[t]], {t, 0, x}]
> g[x_] := Integrate[Sqrt[1 + Cos[t]], {t, 0, x}]
>
> Then f[2Pi] is 0 (wrong) and g[2Pi] if 4Sqrt[2] (correct). Of course
> f[x]==g[x] returns True.
>
> Garry Helzer
> Department of  Mathematics
> University of Maryland
> 1303 Math Bldg
> College Park, MD 20742-4015
>
>
>

--
majort at cox-internet.com
Bobby R. Treat

```

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