Quiz: calculating a definite integral
01-02-2014, 11:34 AM (This post was last modified: 01-02-2014 11:36 AM by Gerson W. Barbosa.)
Post: #24
 Gerson W. Barbosa Senior Member Posts: 1,537 Joined: Dec 2013
RE: Quiz: calculating a definite integral
(01-01-2014 10:31 PM)Thomas Klemm Wrote:
(12-31-2013 10:24 AM)peacecalc Wrote:  calculating the integrand: instead of $$x^{-x}$$ as $$\exp(-x\cdot\ln(x))$$
That's a step into the right direction.
What's the next? What's $$\exp(t)$$?

Cheers
Thomas

e^t=1+t+1/2*t^2+1/6*t^3+...
=1-x*lnx+x^2*(lnx)^2/2-...
which, upon integration over [0..1], yields
1+1/2^2+1/3^3+1/4^4+...
The first ten terms add up to
1.29128599706
Cheers from Camboriú, Brazil
Gerson.
PS: Sorry for not elaborating enough (slowly typing this on an iphone)
Ought to be at the beach instead :-)
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