Re: Mathematica gives bad integral ??
- To: mathgroup at smc.vnet.net
- Subject: [mg24332] Re: Mathematica gives bad integral ??
- From: "Kevin J. McCann" <Kevin.McCann at jhuapl.edu>
- Date: Sun, 9 Jul 2000 04:52:40 -0400 (EDT)
- Organization: Johns Hopkins University Applied Physics Lab, Laurel, MD, USA
- References: <8k3n38$3pk@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I suspect this has to do with branches of complex functions. I tried using both Mathematica and the Schaum answer on definite integrals, e.g. {x,1,2}, and got the same answers. Without spending a lot of time, I do not see how to easily find the relationship between the two answers. Kevin "J.R. Chaffer" wrote: > > Hi, this newbie gets erroneous results with Mathematica > 4.0 (for students), with the following integral. Hopefully > someone can tell me why, and what I may be doing > wrong. I have tried "Assumptions -> x e Reals", or > x > 0, with same results. Integral in question is, > > Integrate[1/Sqrt[1-Sin[2x]]] > > The result is somewhat involved, instead of the expected > result (Schaum, "Calculus" 4E, p. 297), > > integral = - (1/Sqrt[2])Log[Abs[Csc[Pi/4-x]-Cot[Pi/4-x]]] > > One expects to get differing forms with any computer > algebra system, since there are so many equivalent forms > of algebraic expressions. However, Mathematica's form > and the Schaum (correct) form differ by significant > numerical values, as plotting shows (i.e., not some E-16 > or some such). > > Further, and what really seems wrong, is that when one > differentiates Mathematica's result for the integral, one > does NOT get the original integrand, or anything even > close, numerically. > > So, I am confused. Anyone who knows the explanation > would be welcome to share it. > > Thank you. > > John Chaffer