The equation of the above ellipse is 



We will just find the area of the part in the first quadrant,
and then by symmetry multiply by 4 to get the area in all four 
quadrants.  We will use:




We solve for y:



Multiply through by 







Take positive square roots of both sides:







We use trigonometric substitution:
sqrt(a^2-x^2)





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To substitute we eill also change the limits from
limits on x to limits on @:

When ,  and
when ,  


Substituting

 








  
















Edwin