ERASMUS WILL ANSWER THE GODS OF BARBEAU'S BOX.
1. USE A DOUBLE INTEGRAL TO FIND THE AREA OF THE LEMNISCATE r=sqrt(cos(2theta))
HENCE The integral is int(theta= 0 to PI/4){int(r= 0 to sqrt(cos(2theta)) r dr} dtheta.
I WILL NOT CALCULATE THIS, SINCE I HAVE RUN OUT OF ILLEGAL SUBSTANCES AND LOST THE TRANCE THAT GUIDED MY HAND. YET LIKE THE ORACLE AT DELPHI I HAVE GLANCED CYRPTIC HINTS THAT MAY AID YOU.
1. GRAPH IT.
http://www.answers.com/topic/lemnisc...cos-2theta-png
2. SINCE IT IS ABOUT THE X AXIS YOU MAY HAVE TO USE SYMMETRY TO FIND YOUR ANSWER... I.E. DOUBLE YOUR ANSWER.
THAT IS ALL ERASMUS SHALL DO. ERASMUS IS FAR TOO IMPORTANT TO ANSWER SIMPLE MATH EQUATIONS..BESIDES THERE ARE EASIER WAYS TO GAINING ENLIGHTENMENT GENESIS. JOIN MY REVOLUTION AND ALL WILL BECOME CLEAR.