But I am still missing a sound answer from the operators of the pages ...

Maple can find a symbolic solution (in term of hypergeometric 1F2), 
but exceeds my patients in computing the numerical value.

  assume( r::posint);
  Int(sin(x^r),x=0..10);
  value(%); #simplify(%);
  eval(%, r=19);

                                                           r
           (1 + r)            1 + r         3 r + 1     100
         10        hypergeom([-----], [3/2, -------], - ----)
                               2 r            2 r        4
         ----------------------------------------------------
                                1 + r

After playing a lot (!) the following seems to be a way

  Int(sin(x^r),x=0..10);
  Change(%, x^r=t,t):

                          r         /  r - 1\
                        10          |- -----|
                       /            \    r  /
                      |     sin(t) t
                      |     ----------------- dt
                      |             r
                      |
                     /
                       0

For r=19 the power function contributes almost nothing for that
oscillating integral and is decaying so (without proof!) one can
switch to the whole positive Reals:

  Int(sin(t)*t^(-(r-1)/r)/r,t = 0 .. infinity);
  value(%);
  eval(%, r=19);
  evalf(%);


                            1/19   1/2       10
                           2     Pi    GAMMA(--)
                                             19
                      1/38 ---------------------
                                       37
                                 GAMMA(--)
                                       38


                          0.080286517328223

But - as already said - one has to provide an estimation for the 'tail'.


Note, that then this is the same as Int(sin(x^19),x=0..infinity), but in
that formulation I do never see a justification for |tail integral| < eps.

@JacquesC I added "bug" as tag to some of my contributions (as far as the bug is present in Maple 12) and for me that was only possible by editting (a weakness of the board software and/or its current implementation).

Now - having a new board and style of communication - it is time to give that role back.

Gruß
Axel

@pagan 

IIRC Excel initializes to zero (so the posted code does not much ...)

@pagan 

IIRC Excel initializes to zero (so the posted code does not much ...)

That is certainly not only trivial stuff, just an active topic: "A ring such that all projectives are stably free but not all projectives are free?", http://mathoverflow.net/questions/27424/a-ring-such-that-all-projectives-are-stably-free-but-not-all-projectives-are-free

Actually it is about the Grothendieck group, and the answer by Kumar (quite well known in commutative algebra) shows people you rarely can watch at sci.math.

BTW: if remember correctly the 'classical' proof for his answer is via algebraic topology "Satz vom Igel" (do not know the English name) and the sphere in R^3, while he his citation is Swan, Annals and *very* deep.

@pagan 

An example with basic rating, which is fast and provides structured information and easy to use (missing some features here) is http://www.nuclearphynance.com/ It simply works. And it is living, active.

@Alec Mihailovs ... or: I have my own attitude towards marketing and people working there

To explain: while working in sales I once enjoyed a Swiss training (in some sense stemming
from attidues of the Swiss Army). The advantage is: it applies to both sides (though so it was
not so much the intention).

But if you observe the whole process, then can you observe two things? Will is in front and
defending, the other is back, almost quiet. There are at least two situations, where that is
typical: good guy / bad guy - and hierarchic structures.

Now it is late, bye.

@Alec Mihailovs 

Well, assuming that arguing has an essential effect assumes that your counter part is open minded in some (at least minor) sense.

@Alec Mihailovs 

It is a kind of number fetish, addicted to statistics and I guess you are teasing (no?). But maintainers, marketing and 'mgmt' love it.

If one would really need that, then on usenet one would be lost: two positives and one for trash is enough for me.

And I do not see why mine should be between Robert Israel and Joe Riel ... funny. Besides others, which I appreciate pretty much. So what.

@Will: you should not use Port 81 here.

....................................... (a body with at least 15 characters)

... like blogs and subscriptions, I can not even find my uploaded files.

In short: the new appearanceis not satisfactory for me and I hope it will be improved.

Sorry to say that. But I am sure improvement is possible.

@Will 

The given link gives an empty content. Do I understand correctly: my old subscriptions are gone?

my access as moderator is gone ...

http://www.mapleprimes.com/posts/36010-Moderator-List

macht nix, kann auch jemand anders machen ...