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Quiz: calculating a definite integral
01-02-2014, 11:55 AM
Post: #25
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.

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RE: Quiz: calculating a definite integral - Thomas Klemm - 01-02-2014 11:55 AM

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