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: ------------------------------------------ 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) ------------------------------------------- How many other bugs lurk in integrands containing Sqrt? Thanks in advance, W. Craig Carter wcraig at pruffle.nist.gov