Re: Re: Integrating Abs[Sin[]^2]
- To: mathgroup at smc.vnet.net
- Subject: [mg38971] Re: [mg38936] Re: Integrating Abs[Sin[]^2]
- From: Dr Bob <drbob at bigfoot.com>
- Date: Thu, 23 Jan 2003 08:03:43 -0500 (EST)
- References: <b032m9$mv4$1@smc.vnet.net> <b05qsi$2a7$1@smc.vnet.net> <b0jg1t$t97$1@smc.vnet.net> <200301221109.GAA05214@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Mathematica is NOT giving wrong answers in this case. It is assuming (non-zero) real parameters and giving the right answer in that case. Bobby On Wed, 22 Jan 2003 06:09:24 -0500 (EST), David W. Cantrell <DWCantrell at sigmaxi.org> wrote: > Jos R Bergervoet <antispam at nospam.com> wrote: >> David W. Cantrell wrote: >> > >> > Jos R Bergervoet <jos.bergervoet at philips.no_s_p_a_m.com> >> >> >> >> result = Integrate[ Abs[Sin[k x]]^2, {x,0,1}] >> >> N[ result /. k->I+1 ] >> >> >> >> (* Analytical approach gives 0.261044 + 0.616283 I, WRONG !!! *) >> >> >> >> k=I+1; NIntegrate[ Abs[Sin[k x]^2], {x,0,1}] >> >> >> >> (* Numerical check gives 0.679391 *) >> >> >> ... >> >> What should I do to circumvent such errors? >> > >> > One thing that works in Mathematica (as well as in the other CAS) is >> to >> > >> > Integrate[ Abs[Sin[(a+b*I) x]]^2, {x,0,1}]. >> > >> > This gives (a*Sinh[2*b] - b*Sin[2*a]) / (4*a*b), >> > >> > which agrees with your result below. >> >> But again it is wrong! It only is correct if a and b happen >> to be real quantities, which is nowhere stated! > > Well, let me state it now here: > > I was merely trying to provide a "workaround" which would give you a > correct result in the event that your coefficient k was complex. (I was > not trying in any way to exonerate Mathematica!) In that event, k may be > written, _without loss of generality_, as a+b*I, where a and b are both > REAL. > >> So the main question still is: Why is Mathematica making >> these very silly errors? One could expect it from an early >> version of a product, but that is not what Mathematica 4.x >> is! > > Yes, the main question remains. > > David > > -- majort at cox-internet.com Bobby R. Treat
- References:
- Re: Integrating Abs[Sin[]^2]
- From: "David W. Cantrell" <DWCantrell@sigmaxi.org>
- Re: Integrating Abs[Sin[]^2]