When is the area of this region bigger than the area of this one?

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Consider two functions \[f(x) = a - x^2,\] \[g(x) = x^4 - a.\]

For precisely which values of \(a > 0\) is the area of the region bounded by the \(x\)-axis and the curve \(y = f(x)\) bigger than the area of the region bounded by the \(x\)-axis and curve \(y = g(x)\)?

1. all values of \(a\),
2. \(a > 1\),
3. \(a > \dfrac{6}{5}\),
4. \(a > \left(\dfrac{4}{3}\right)^{3/2}\),
5. \(a > \left(\dfrac{6}{5}\right)^4\).

Drawing a diagram might help to visualise what is happening here.

Can we use calculus to find the areas mentioned?

What do we know about areas below the \(x\)-axis?