Re: Simple integral wrong

*To*: mathgroup at smc.vnet.net*Subject*: [mg25073] Re: Simple integral wrong*From*: Paul Cally <cally at kronos.maths.monash.edu.au>*Date*: Thu, 7 Sep 2000 22:28:17 -0400 (EDT)*Organization*: Monash University*References*: <8opmr5$15@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Paul Cally wrote: > Try integrating | cos u| from u=0 to u = Pi x. Despite the integrand > being everywhere > non-negative, Mathematica 4 gives a result which jumps DOWNWARDS by 2 at > > x=1/2, 3/2, 5/2, .... I thought these simple integration errors had been > sorted out by > Wolfram years ago! > > Paul Cally > > -- > > +--------------------------------------------------------------------------+ > |Assoc Prof Paul Cally | Ph: +61 3 9905-4471 | > |Dept of Mathematics & Statistics | Fax: +61 3 9905-3867 | > |Monash University | paul.cally at sci.monash.edu.au | > |PO Box 28M, Victoria 3800 | | > |AUSTRALIA | http://www.maths.monash.edu.au/~cally/ | > +--------------------------------------------------------------------------+ I have had a number or queries about this. Sorry I hadn't made it clearer. Here is the full story: A couple of people told me that Plot[Integrate[Abs[Cos[u]], {u, 0, x Pi]}], {x, 0, 3}] works fine. The result is monotonic increasing as expected. But try Plot[Evaluate[Integrate[Abs[Cos[u]],{u,0,Pi*x}]],{x,0,3}] and see what happens! The evaluate forces Mathematica to do the integral symbolically. It was doing it numerically without the Evaluate. Or just type Integrate[Abs[Cos[u]],{u,0,Pi x}] Mathematica 4 returns 2 Out[1]= Sqrt[Cos[Pi x] ] Tan[Pi x] (Actually, I don't think Mathematica 3 can do it at all.) This plots as a saw-tooth. The true solution should be Sqrt[Cos[Pi x]^2] Tan[Pi x] + 2 Floor[x + 1/2] Mathematica misses the step functions necessary to make the solution continuous. Thanks for your interest, Paul Cally -- +--------------------------------------------------------------------------+ |Assoc Prof Paul Cally | Ph: +61 3 9905-4471 | |Dept of Mathematics & Statistics | Fax: +61 3 9905-3867 | |Monash University | paul.cally at sci.monash.edu.au | |PO Box 28M, Victoria 3800 | | |AUSTRALIA | http://www.maths.monash.edu.au/~cally/ | +--------------------------------------------------------------------------+