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integration puzzlement
*To*: mathgroup at yoda.physics.unc.edu
*Subject*: integration puzzlement
*From*: wcraig at pruffle.nist.gov (W. Craig Carter)
*Date*: Thu, 17 Sep 92 14:54:49 EDT
I have a puzzle that I can't figure out:
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Mathematica 2.0 for SPARC
Copyright 1988-91 Wolfram Research, Inc.
-- X11 windows graphics initialized --
g[a_, b_] := Integrate[ x / Sqrt[ 1 - x^2 ], {x, a, b} ]
g[a,b] gets Sqrt[1 - a^2] - Sqrt[1 - b^2] (*Correct!*)
g[a,1] gets 1 (*NOT!*)
g[1,a] gets -Sqrt[1 - a^2] (*Correct!*)
Hints:
1) MathI doesn't get this error,
2) Using Unprotect[Sqrt];Sqrt[x_^y_] := x^(y/2)/;EvenQ[y];Protect[Sqrt]; and so on for Power
doesn't help
3) Using instead, f [a_, b_] := Integrate[ Sqrt[ x^2 / (1 - x^2) ], {x, a, b} ]
i.e, the same integrand, works (but is a pain to simpify the result)
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How many other bugs lurk in integrands containing Sqrt?
Thanks in advance, W. Craig Carter wcraig at pruffle.nist.gov
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