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>*Reply-to*: drbob at bigfoot.com*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

**References**:**Antiderivatives and Definite Integrals***From:*Garry Helzer <gah@math.umd.edu>