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

```

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