In the language of Calculus, the area between two curves is essentially a difference of integrals. The applications of this calculation range from macroeconomic tax models to signal analysis.

What is the area of the region bounded by the curve \(x= -{y}^2+100\) and the \(y\)-axis ?

What is the area of the region bounded by the curve \(x= -6y(y-4)\) and the \(y\)-axis ?

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