Re[2]: Re: Simplification of definite integral?
- To: mathgroup at smc.vnet.net
- Subject: [mg40739] Re[2]: [mg40701] Re: Simplification of definite integral?
- From: Vladimir Bondarenko <vvb at mail.strace.net>
- Date: Tue, 15 Apr 2003 04:00:34 -0400 (EDT)
- References: <001801c30305$36b29960$53813e44@Dell>
- Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
- Sender: owner-wri-mathgroup at wolfram.com
"David W. Cantrell" <DWCantrell at sigmaxi.org> wrote on Tuesday, April 15, 2003, 1:12:22 AM: DWC> any direct way to get Mathematica to give a correct answer for DWC> this integral. Suggestions anyone? This bug boils down to a fundamental bug the long-liver I wrote to WRI about in 2001 N[Integrate[Sin[z]/(z^2 - 1), {z, 2, Infinity}]] -0.797165 - 1.32178 I which exists in all versions since Mathematica Windows 387 2.2 (April 9, 1993) to Mathematica 4.2 for Microsoft Windows (August 23, 2002). A decennial is coming soon. However, there is life there is hope ;) I was told that it seems Wolfram is going to release Mathematica 5 in the near future; maybe they would fix the mean thing... I am resending it to support at wolfram.com one more time, just in case. As for your request, my solution is (please observe Re which means that it seems there is no straightforward way to solve your task) int = Integrate[Sin[z - 1]/(z - 1) Sin[z + 1]/(z + 1), {z, 2, a}]; << Calculus`Limit` ans = FullSimplify[Re[Limit[int, a -> Infinity]]] (Cos[2]*(CosIntegral[2] - CosIntegral[6] + Log[3]) + Sin[2]*(Pi + SinIntegral[-2] - SinIntegral[6]))/4 N[ans] -0.140037 NIntegrate[Sin[z - 1]/(z - 1) Sin[z + 1]/(z + 1), {z, 2, Infinity}, Method -> QuasiMonteCarlo] Sum[NIntegrate[Sin[z - 1]/(z - 1) Sin[z + 1]/(z + 1), {z, 0 + n, 1 + n}], {n, 2, 99999}] -0.140004 -0.140035 Best wishes, Vladimir Bondarenko Mathematical and Production Director Symbolic Testing Group Web : http://www.CAS-testing.org/ GEMM Project (95% ready) Email: vvb at mail.strace.net Voice: (380)-652-447325 Mon-Fri 6 a.m. - 3 p.m. GMT Mail : 76 Zalesskaya Str, Simferopol, Crimea, Ukraine