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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: 1,245 Registered: 4/26/08
Re: The Charlwood Fifty
Posted: Jun 6, 2013 4:19 PM
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"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.

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