[Math4u] Re: Curious definite integral relationship

Jim,

The fun is in showing the relationship. You don't have to find the
actual values of the integrals to do it.

-- Rick

--- In Math4u@yahoogroups.com, "w7anf" <cherry@...> wrote:
>
> 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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