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MathGroup Archive 2006

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Oh, those complex values!!!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72068] Oh, those complex values!!!
  • From: aaronfude at gmail.com
  • Date: Mon, 11 Dec 2006 04:54:38 -0500 (EST)

Integrating a real function, getting complex values again. How to get
the correct answer here? How to systematically avoid this pitfall?

f=x Log[a+b x+Sqrt[c+2d x+x^2]];
t = Assuming[c>d^2&&a>0&&b>0,Integrate[f, x]];
u=t/.a\[Rule]2/.b\[Rule]2/.c\[Rule]10/.d\[Rule]1;

N[u/.x\[Rule]1-u/.x\[Rule]0]
9.50705\[InvisibleSpace]-29.7626 \[ImaginaryI]

NIntegrate[f/.a\[Rule]2/.b\[Rule]2/.c\[Rule]10/.d\[Rule]1, {x, 0, 1}]
0.954442

Many thanks in advance!

Aaron Fude


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