[Math4u] Curious definite integral relationship

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

Yahoo! Groups Links

<*> To visit your group on the web, go to:

http://groups.yahoo.com/group/Math4u/

<*> Your email settings:
Individual Email | Traditional

<*> To change settings online go to:

http://groups.yahoo.com/group/Math4u/join

(Yahoo! ID required)

<*> To change settings via email:
mailto:Math4u-digest@yahoogroups.com
mailto:Math4u-fullfeatured@yahoogroups.com

<*> To unsubscribe from this group, send an email to:
Math4u-unsubscribe@yahoogroups.com

<*> Your use of Yahoo! Groups is subject to:

http://docs.yahoo.com/info/terms/