Re: Bug in Integrate?

*To*: mathgroup at yoda.ncsa.uiuc.edu*Subject*: Re: Bug in Integrate?*From*: uunet!gte.com!blachman%gtewd.dnet (NELSON M. BLACHMAN)*Date*: Thu, 16 Aug 90 14:12:17 -0400

Using the well knwon formula for the sine of half of an angle, I notice that Integrate[ Sqrt[(1 - Cos[theta])^2 + Sin[theta]^2 ], {theta, 0, 2 Pi}] = Integrate[ Sqrt[2 - 2 Cos[theta] ], {theta, 0, 2 Pi}] = Integrate[ 2 Sin[theta/2], {theta, 0, 2 Pi}] = Integrate[ 4 Sin[theta/2], {theta/2, 0, Pi}] = Integrate[ 4 Sin[phi], {phi, 0, Pi}] = -4 Cos[Pi] + 4 Cos[0] = 8 . There seems to be nothing wrong with NIntegrate. Why does Integrate get the value 0?? It's troubles could be sured by a high-school course in trigonometry so that it might carry out the foregoing simplification. A different problem: We recently got VAX-VMS Mathematica but haven't figured out yet how to get its Edit...[ ] features to work; the suggestions in the User's Guide regarding assigning EDITOR the value EDIT/EDT, etc., don't succeed. Nelson M. Blachman blachman%gtewd.dnet at gte.com GTE Government Systems Corp. Mountain View, California