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Antiderivatives and Definite Integrals

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  • Subject: [mg39670] Antiderivatives and Definite Integrals
  • From: Garry Helzer <gah at>
  • Date: Sat, 1 Mar 2003 02:47:47 -0500 (EST)
  • Sender: owner-wri-mathgroup at

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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