Problem
Consider the functions f, g: R → R defined by f(x) = x2 + 5/12, and
g(x) = \( \begin{cases} 2(1-4|x|/3) & \text{if } |x| \le 3/4 \\ 0 & \text{if } |x| > 3/4 \\ \end{cases}\)
If α is the area of the region {(x, y) ∈ R x R : |x| ≤ 3/4, 0 ≤ y ≤ min{f(x), g(x)}}, then find the value of 9α.