Re: Integrate malfunction?

*To*: mathgroup at smc.vnet.net*Subject*: [mg33872] Re: [mg33860] Integrate malfunction?*From*: BobHanlon at aol.com*Date*: Sun, 21 Apr 2002 06:12:18 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 4/20/02 4:28:27 AM, sbstory at unity.ncsu.edu writes: >I recently had to do an integral which should evaluate to be a very very >small quantity. The function is always positive, but the integral gives >me a >negative number. I think this is a malfunction of some sort. Here's the >code: > >amu = 1.661*10^-27 >nitrogen = 28*amu >k = 1.381*10^-23 >t = 1000 > >Integrate[ > 4 Pi ((nitrogen/(2 Pi k t))^(3/2)) x^2 Exp[(-1 nitrogen x^2)/(2 k t)], >{x, >11000, Infinity}] > >Out[13]= -5.878291776559734*10^-16 > >does anyone know why this is happening? i tried NIntegrate instead, but >it >said: > >General::"unfl": "Underflow occurred in computation." > Use higher precision. For example, you can use rational numbers amu=1661*10^-30; nitrogen=28*amu; k=1381*10^-26; t=1000; N[FullSimplify[Integrate[4*Pi*(nitrogen/(2*Pi*k*t))^(3/2)* x^2*Exp[-(nitrogen*x^2)/(2*k*t)], {x, 11000, Infinity}]]] 5.275254153535021*^-88 Note that for maximum precision you want to use FullSimplify before converting to a numerical result. Bob Hanlon Chantilly, VA USA