Re: TI-M: Integral of x^x

To: ti-math@lists.ticalc.org
Subject: Re: TI-M: Integral of x^x
From: Andy Selle <aselle@ticalc.org>
Date: Tue, 30 May 2000 03:47:56 +0200 (MET DST)
In-Reply-To: <6b.4e18620.266475e3@aol.com>
Reply-To: ti-math@lists.ticalc.org

Well sure... definite integrals can exist as long as the function values
within the limits of integration are bounded.  That is to say you can't
have any singularities if you want to integrate of a <= x <= b... i.e.
this is bad. .. integral(1/x,x,-1,1)... The problem, though is that this
can only be done on a case by case numerical way.  You cannot establish a
explicit simplification of the indefinite integral.  In fact, the definite
integral from 0 to infinity of x^x does not exist, because x^x is
unbounded as x->infinity.

--
Andy Selle <aselle@ticalc.org>
   Programming and System Administration, Survey Editor, Accounts Manager
   the ticalc.org project - http://www.ticalc.org/

On Mon, 29 May 2000 Force15@aol.com wrote:

> 
> I was doing some research today about Euler's identity and I came across the 
> x^x integral. In fact, it can be solved, according to the book An Imaginary 
> Tale The Story of sqrt(-1) by Paul J. Nahim. On p. 145-146, the author 
> describes the process involved to solve it, I think as done by de Moivre (but 
> I'm not sure). I didn't have enough time to really check it out so, but I did 
> write down the answer: the indefinite integral = the Sum of 
> [(-1)^n]/[(n+1)^(n+1)] from zero to infinity. The first few terms are 
> 1-1/2^2+1/3^3-1/4^4+1/5^5........ you get the idea. Just in case anyone 
> cares, the definite integral from zero to one = 0.78343.......  Hope this 
> helps!
> 
> God Bless,
> Will Landry
> 
>

References:

Re: TI-M: Integral of x^x

From: Force15@aol.com