Question

Consider the functions $f, g: R \rightarrow R$ defined by
$f(x)=x^2+\frac{5}{12} \text { and } g(x)= \begin{cases} 2\left(1-\frac{4|x|}{3}\right), & |x| \leq \frac{3}{4}, \\\0, & |x|>\frac{3}{4}. \end{cases}$
If $\alpha$ is the area of the region \left\\{( x , y ) \in R \times R :| x | \leq \frac{3}{4}, 0 \leq y \leq \min \\{f( x ), g( x )\\}\right\\}, then the value of $9 \alpha$ is ____.

Answer 1

The answer is 6.