Re: Re: Integrating Abs[Sin[]^2]
- To: mathgroup at smc.vnet.net
- Subject: [mg38995] Re: [mg38936] Re: Integrating Abs[Sin[]^2]
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Fri, 24 Jan 2003 05:04:00 -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> <oprjevv7tramtwdy@smtp.cox-internet.com>
- Sender: owner-wri-mathgroup at wolfram.com
"Dr Bob" <drbob at bigfoot.com> wrote: > Mathematica is NOT giving wrong answers in this case. > > It is assuming (non-zero) real parameters and giving the right > answer in that case. Whether Mathematica is or is not giving a "wrong" answer in the case result = Integrate[ Abs[Sin[k x]]^2, {x,0,1}]; N[ result /. k->I+1 ] depends upon whether it is or is not appropriate for Mathematica to make a default assumption that k is a nonzero real. IMO, that could be debated. But surely, as I noted previously in this thread, Mathematica -- at least version 4.2 for Windows -- does give a wrong answer for result = Integrate[ Abs[Sin[k x]]^2, {x,0,1}, Assumptions-> Element[k, Complexes]; N[ result /. k->I+1 ]. I do not see how the incorrectness of this can be debated (other than to say that Mathematica should be allowed to ignore an _explicitly stated_ assumption!) David > 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.
- References:
- Re: Integrating Abs[Sin[]^2]
- From: "David W. Cantrell" <DWCantrell@sigmaxi.org>
- Re: Integrating Abs[Sin[]^2]