Quiz: calculating a definite integral
01-02-2014, 11:55 AM
Post: #25
 Thomas Klemm Senior Member Posts: 1,542 Joined: Dec 2013
RE: Quiz: calculating a definite integral
(01-02-2014 10:12 AM)peacecalc Wrote:  e is approximatly 3, is that enough?
How do you think we can get the result to 10 or 12 places?
I'd prefer: $e= \frac{1}{0!}+ \frac{1}{1!}+ \frac{1}{2!}+ \frac{1}{3!}+\cdots$
One method when dealing with difficult problems is breaking them into smaller parts. Hopefully these are easier to handle. In this case we have to integrate $$x^{-x}$$ which isn't easy. One method to break it apart is using series. Use $$e^{-x\log(x)}$$ and the power series of $$e^x$$. Swap the order of integration and summation. Integrate each of the parts and plug everything together and you have a nice formula which can be used with the calculator.

Cheers
Thomas
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 Messages In This Thread Quiz: calculating a definite integral - Thomas Klemm - 12-30-2013, 09:37 PM RE: Quiz: calculating a defined integral - John Smitherman - 12-30-2013, 10:46 PM RE: Quiz: calculating a defined integral - W_Max - 12-30-2013, 11:44 PM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 06:37 AM RE: Quiz: calculating a defined integral - Namir - 12-31-2013, 04:24 AM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 04:56 AM RE: Quiz: calculating a defined integral - walter b - 12-31-2013, 08:54 AM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 09:14 AM RE: Quiz: calculating a defined integral - walter b - 12-31-2013, 10:12 AM RE: Quiz: calculating a defined integral - Paul Dale - 12-31-2013, 07:13 AM RE: Quiz: calculating a defined integral - peacecalc - 12-31-2013, 10:24 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-01-2014, 10:31 PM RE: Quiz: calculating a definite integral - walter b - 01-02-2014, 08:11 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-02-2014, 06:09 PM RE: Quiz: calculating a definite integral - Gerson W. Barbosa - 01-02-2014, 11:34 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-02-2014, 01:14 PM RE: Quiz: calculating a definite integral - Gerson W. Barbosa - 01-03-2014, 01:49 AM RE: Quiz: calculating a defined integral - peacecalc - 12-31-2013, 10:57 AM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 01:14 PM RE: Quiz: calculating a definite integral - Gerson W. Barbosa - 01-16-2014, 08:21 PM RE: Quiz: calculating a defined integral - Paul Dale - 12-31-2013, 01:29 PM RE: Quiz: calculating a defined integral - walter b - 12-31-2013, 02:16 PM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 06:01 PM RE: Quiz: calculating a definite integral - Ángel Martin - 01-03-2014, 07:20 AM RE: Quiz: calculating a defined integral - peacecalc - 12-31-2013, 02:20 PM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 05:55 PM RE: Quiz: calculating a definite integral - peacecalc - 01-02-2014, 08:36 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-02-2014, 09:42 AM RE: Quiz: calculating a definite integral - peacecalc - 01-02-2014, 10:12 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-02-2014 11:55 AM RE: Quiz: calculating a definite integral - Bunuel66 - 01-02-2014, 11:39 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 05:18 AM RE: Quiz: calculating a definite integral - walter b - 01-03-2014, 06:08 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 07:03 AM RE: Quiz: calculating a definite integral - Bunuel66 - 01-03-2014, 11:42 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 12:47 PM RE: Quiz: calculating a definite integral - Bunuel66 - 01-03-2014, 01:29 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 02:50 PM RE: Quiz: calculating a definite integral - Bunuel66 - 01-03-2014, 05:38 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 08:39 PM RE: Quiz: calculating a definite integral - Bunuel66 - 01-03-2014, 09:04 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-06-2014, 10:28 AM RE: Quiz: calculating a definite integral - Bunuel66 - 01-07-2014, 06:12 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-09-2014, 07:45 AM RE: Quiz: calculating a definite integral - W_Max - 01-03-2014, 08:03 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 09:32 PM RE: Quiz: calculating a definite integral - W_Max - 01-03-2014, 11:08 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-14-2014, 02:31 PM RE: Quiz: calculating a definite integral - walter b - 01-14-2014, 02:53 PM

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