Re: confusion with triple integral...

• To: mathgroup at smc.vnet.net
• Subject: [mg32487] Re: [mg32469] confusion with triple integral...
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Wed, 23 Jan 2002 01:00:06 -0500 (EST)
• References: <200201220819.DAA07095@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

correct answer that Mathematica returns (in my computer, anyway) is 5 Pi,
and this may be checked easily. The integrand doesn't depend on y, so in
fact you have only a double integral whose value is equal to 2.5. On
multiplying this by the integral of dy from 0 to 2 Pi, which is equal to 2
Pi, you get 5 Pi. Now, this is displayed as either 5 Pi or 15.708...(the
numerical value of 5 Pi) according to whether I use ArcCos[1/4] or
ArcCos[0.25] (or, equivalently, ArcCos[1/4]//N) in the corresponding limit.

Tomas Garza
Mexico City

----- Original Message -----
To: mathgroup at smc.vnet.net
Subject: [mg32487] [mg32469] confusion with triple integral...

> 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
>