Re: A negative volume!

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re: A negative volume!*From*: ags at seaman.cc.purdue.edu (Dave Seaman)*Date*: Sat, 14 Mar 92 11:38:19 -0500

>> >Anybody have any suggestions on how to avoid this kind of problem? > >> A change in the order of integration seems to do the trick. > >Doing the integral by hand also does the trick. I think the question >is how to increase the reliability of Mathematica's definite >integrals, not to get the answer to one particular integral. > >Silvio I fail to see any practical difference between the observations "A change in order works." and "Integrating by hand words." Both point out in unmistakeable terms that there is a problem in Integrate[], and neither offers a solution. My observation was intended to offer some insight into what went wrong. More precisely, the original poster has pointed out that the third integral in his computation leads to an antiderivative that is piecewise continuous, with discontinuities at both endpoints of the interval of integration, and Mathematica seems to have used the wrong one-sided limits. Dave