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MathGroup Archive 2002

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Re: confusion with triple integral...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32481] Re: [mg32469] confusion with triple integral...
  • From: BobHanlon at aol.com
  • Date: Wed, 23 Jan 2002 00:59:56 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 1/22/02 3:42:57 AM, BradleyS at Harker.org writes:

>Please consider the Integral[r^2Sin[x]drdxdy] with limits as follows:
>[0,2Pi]for y, [0,ArcCos[1/4]] for x and [0,1/Cos[x]] for r.  Mathematica
>returns
>27Pi, which is correct.  But, if instead of using ArcCos[1/4], I use either
>ArcCos[0.25] or ArcCos[1/4]//N in the limits, Mathematica returns 43Pi.
> Any idea
>why?j
>

I get 5Pi for each.

Clear[r,x,y]

Integrate[r^2*Sin[x],{y,0, 2Pi},{x,0,ArcCos[1/4]},{r,0,1/Cos[x]}]

5*Pi

%==Integrate[r^2*Sin[x],{y,0,2Pi},{x,0, ArcCos[0.25]},{r,0,1/Cos[x]}]

True

%%==Integrate[r^2*Sin[x],{y,0, 2Pi},{x,0, ArcCos[1/4]//N},{r,0,1/Cos[x]}]

True


Bob Hanlon
Chantilly, VA  USA


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