Re: Correction on confusion with triple integral...

*To*: mathgroup at smc.vnet.net*Subject*: [mg32511] Re: [mg32488] Correction on confusion with triple integral...*From*: Tomas Garza <tgarza01 at prodigy.net.mx>*Date*: Thu, 24 Jan 2002 05:21:06 -0500 (EST)*References*: <200201230600.BAA18200@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Wow! You've really hit on something weird, which has to do - I guess - with the fact that the lower limit in the innermost integral, i.e., 1/Cos[x], is indeterminate at x = ArcCos[1/4]. If you evaluate the innermost integral you get In[1]:= Integrate[r^2, {r, 1/Cos[x], 4}] Out[1]= 64/3 - Sec[x]^3/3 so that the integrand in the middle integral is In[2]:= Sin[x]*Integrate[r^2, {r, 1/Cos[x], 4}] Out[2]= Sin[x]*(64/3 - Sec[x]^3/3) The fishy thing is that the value of the definite integral of this last function is different according to whether it is obtained using Integrate or NIntegrate! In[3]:= Integrate[Sin[x]*(64/3-Sec[x]^3/3),{x,0,ArcCos[0.25]}] Out[3]= 43/2 In[4]:= NIntegrate[Sin[x]*(64/3-Sec[x]^3/3),{x,0,ArcCos[0.25]}] Out[4]= 13.5 where the second one is correct. Let's hope that one of the Mathematica gurus will give us some explanation. Tomas Garza Mexico City ----- Original Message ----- From: "Bradley Stoll" <BradleyS at harker.org> To: mathgroup at smc.vnet.net Subject: [mg32511] [mg32488] Correction on confusion with triple integral... > My apologies. After reading Bob's message I realized I had a typo. The > limits on r were supposed to be [1/Cos[x],4], not [0,1/Cos[x]]. So, here is > the corrected problem... > > Please consider the Integral[r^2Sin[x]drdxdy] with limits as follows: > > [0,2Pi]for y, [0,ArcCos[1/4]] for x and [1/Cos[x],4] 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? >

**References**:**Correction on confusion with triple integral...***From:*Bradley Stoll <BradleyS@Harker.org>