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
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