The curve y= (224755712/(x^2+369664) is called a Witch of Agneesi.  You wish to place a rectangle between the Witch of Agneesi and the x-axis, and you want your rectangle centered on the y-axis.  Assign to area the maximum area of such a rectangle.  Use exact arithmetic (i.e. do not use evalf).  Can someone please tell me how you would go about solving a problem like this?  I have no idea!