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Topic: The Charlwood Fifty
Replies: 52   Last Post: Jun 24, 2013 10:24 PM

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clicliclic@freenet.de

Posts: 978
Registered: 4/26/08
Re: The Charlwood Fifty
Posted: Jun 6, 2013 4:19 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


"Nasser M. Abbasi" schrieb:
>
> On 6/6/2013 11:23 AM, clicliclic@freenet.de wrote:

> >
> > It would have been nice if Prof. Charlwood could have thrown light on
> > problem #49 from his appendix: Did he really want his students to work
> > on an elementary evaluation of INT(ASIN(x*SQRT(1-x^2)), x) and fail?
> >

>
> In http://www.apmaths.uwo.ca/~arich/CharlwoodIntegrationProblems.pdf
>
> #49 is written as INT(ASIN(x/SQRT(1-x^2)), x)
>
> I just checked the Charlwood’s 2008 paper, and it should be as
> you have shown it (i.e. multiplication not division), so there is a
> typo in the above pdf file.
>


Oh, as Albert Rich wrote, he "took the liberty of changing the integrand
of problem #49 from arcsin(x*sqrt(1-x^2)) to arcsin(x/sqrt(1-x^2)). This
was done so all the integrands and antiderivatives in the test-suite
would involve only elementary functions and operators."

>
> [...]
>
> Maple 17 could not seem to be able to do it. returned unevaluated.
>


Strange that Maple can't do this one. Derive 6.10 immediately converts
the integral to

INT(ASIN(x*SQRT(1 - x^2)), x) = x*ASIN(x*SQRT(1 - x^2))
+ SUBST(INT((2*x^2 - 1)/SQRT(x^4 - x^2 + 1), x), x, SQRT(1 - x^2))

and Maple should be able to cope with the algebraic integral that
remains (the Derive integrator has no knowledge of the canonical
elliptic integrals).

Martin.


Date Subject Author
5/23/13
Read The Charlwood Fifty
Albert D. Rich
5/23/13
Read Re: The Charlwood Fifty
Nasser Abbasi
5/23/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/16/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/16/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/17/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/17/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/17/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/17/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/17/13
Read Re: The Charlwood Fifty
Waldek Hebisch
6/18/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/24/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/24/13
Read Re: The Charlwood Fifty
Albert D. Rich
5/23/13
Read Re: The Charlwood Fifty
Albert D. Rich
5/23/13
Read Re: The Charlwood Fifty
Waldek Hebisch
5/24/13
Read Re: The Charlwood Fifty
Andreas Dieckmann
5/25/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/1/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/3/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/6/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/6/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/6/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/8/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/8/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/8/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/8/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/9/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/9/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/9/13
Read Re: The Charlwood Fifty
Albert D. Rich
6/9/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/10/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/10/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/10/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/12/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/13/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/13/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/13/13
Read Re: The Charlwood Fifty
Waldek Hebisch
6/13/13
Read Re: The Charlwood Fifty
Nasser Abbasi
6/13/13
Read Re: The Charlwood Fifty
Waldek Hebisch
6/14/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/14/13
Read Re: The Charlwood Fifty
Waldek Hebisch
6/14/13
Read Re: The Charlwood Fifty / Sage and sympy
Richard Fateman
6/14/13
Read Re: The Charlwood Fifty
clicliclic@freenet.de
6/9/13
Read Re: The Charlwood Fifty and Macsyma
Richard Fateman
6/9/13
Read Re: The Charlwood Fifty and Macsyma
Albert D. Rich
6/9/13
Read Re: The Charlwood Fifty, another Macsyma result
Richard Fateman
6/9/13
Read Re: The Charlwood Fifty, another Macsyma result
Albert D. Rich
6/10/13
Read Re: The Charlwood Fifty, another Macsyma result
Richard Fateman
6/10/13
Read Re: The Charlwood Fifty, another Macsyma result
clicliclic@freenet.de
6/10/13
Read Re: The Charlwood Fifty, another Macsyma result
Waldek Hebisch
6/11/13
Read Re: The Charlwood Fifty, another Macsyma result
Nasser Abbasi
6/11/13
Read Re: The Charlwood Fifty, another Macsyma result
clicliclic@freenet.de
6/11/13
Read Re: The Charlwood Fifty, another Macsyma result
Nasser Abbasi

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