Antiderivatives and Definite Integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg39670] Antiderivatives and Definite Integrals*From*: Garry Helzer <gah at math.umd.edu>*Date*: Sat, 1 Mar 2003 02:47:47 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Antiderivatives and Definite Integrals***From:*Dr Bob <drbob@bigfoot.com>