Consider the function f,g:[tex]\mathbb{R} \to\mathbb{R}[/tex] defined by
[tex] \rm f(x) = {x}^{2} + \frac{5}{12} \: and \: g(x) = \begin{cases}2 \bigg( \rm 1 - \dfrac{4 |x| }{3} \bigg), \: \: \: \: |x| \leq \dfrac{3}{4}, \\ \\ 0, \: \: \: \: \: \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: |x| > \dfrac{3}{4} .\end{cases} [/tex]
If [tex]\alpha[/tex] is the area of the region
[tex] \rm \bigg \{(x,y) \in \mathbb{R} \times \mathbb R : |x| \leq \dfrac{3}{4} ,0 \leq y \leq min \{f(x),g(x) \} \bigg \}[/tex]
then the value of 9[tex]\alpha[/tex]​