[Math4u] Re: Curious definite integral relationship

This should be in my table of elliptic integrals.
Main page:
http://www.getnet.net/~cherry/derive/index.html
Integals h=4 and n=4:
http://www.getnet.net/~cherry/derive/IH4N4N.txt
How to use the tables:
http://www.getnet.net/~cherry/derive/bill.PDF

Jim FitzSimons

--- In Math4u@yahoogroups.com, Rick <rcastrap@...> wrote:
>
> Here is an interesting definite integral relationship found in this
> months Math Horizons, a MAA publication.
>
> I will use Mathematica notation to represent the integrals:
>
> Integral[function,{integration variable,lower limit,upper limit}]
>
> Typically, the integrals of a function and the reciprocal of the
> function bear little relation to each other. The following is an
> interesting exception with applications to the study of elliptic
> functions:
>
> Integral[Sqrt[1-x^4],{x,0,1}] = (2/3)Integral[1/Sqrt[1-x^4],
{x,0,1}]
>
> Anyone want to take a crack at proving this?
>
> -- Rick
>

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