Quiz: calculating a definite integral

[Gerson W. Barbosa]

(01-02-2014 01:14 PM)Thomas Klemm Wrote:  On the WP-34S the \(\sum\) key is just beside the \(\int\) key. You can use the same program:

10.001
\(\sum\) 00

As much as I like the wp-34s, I've preferred the hp 50g for this one:

'∑(n=1;10;1/n^n)'

Also because it can do that:

'X^2*LN(X)^2/2'

INTVX

'(1/3*X^3*LN(X)^2+-2/9*X^3*LN(X)+2/27*X^3)/2'

I'd tried this approach last year, just before leaving, but I quit because I found the overall expression too complicated, even after simplificating the first three terms. Back here again I noticed I was in the right track and decided to give a second look. D'oh! It was only necessary to replace the integration limits for each term individually -- only the rational part of the expressions survive the substitution by 0 and 1 which soon makes the pattern evident--
Thanks for the nice New Year exercise!
Cheers,
Gerson