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MathGroup Archive 2002

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Re: confusion with triple integral...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32485] Re: confusion with triple integral...
  • From: "Dave Snead" <dsnead6 at charter.net>
  • Date: Wed, 23 Jan 2002 01:00:03 -0500 (EST)
  • References: <a2j8o9$79j$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Bradley Stoll <BradleyS at harker.org> wrote in message
news:a2j8o9$79j$1 at smc.vnet.net...
> 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
>
> Bradley Stoll
> San Jose, CA
>

I get a consistent 5 Pi for both these cases

In[3]:=
Integrate[r^2Sin[x],{y,0,2 Pi},{x,0,ArcCos[1/4]},{r,0,1/Cos[x]}]

Out[3]=
5 \[Pi]

In[4]:=
Integrate[r^2Sin[x],{y,0,2 Pi},{x,0,ArcCos[.25]},{r,0,1/Cos[x]}]

Out[4]=
15.708

-- Dave Snead




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