Suppose we have an equation: $${(y\cos{(x)}+u})^{2}+{(-(y\sin{(x)}+v)^3+1)}^{\frac{2}{3}}=1$$
The graph of this implicit relation has two regions, where one part is above the x-axis, and the other part is below the x-axis.
Suppose we're are trying to find the area of the relation above the x-axis, from the domain ${0}\le{x}\le{2\pi}$. How can one solve for the values of u and v that can give the highest area for this equation that's is above the x-axis.
Here is a brief illustration:
Copy and paste the link into the internet:
(C:\Users\Bharathmon\Pictures\Average Radius\AverageRadiusProblem.PNG)
If you find the picture try and use sage to graph the equation above, with respect to u and v.