Well, one way to do that, since this is a closed curve, is to change to polar coordinates: let and [tex]y= r sin(\theta). Now the equation of the curve is [tex]r^4 cos^4(\theta)+ r^4 sin^4(\theta)= 1 or and then the area is given by

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Now, what are thedefinitionsof the Gamma and Beta functions and how do they relate to that integral?