Let the area of the region ${(x, y): 0 \leq x \leq 3,0 \leq y \leq \min {x^{2}+2,2 x+2 } }$ be $A$. Then $12 A$ is equal to
$y=2 x+2$
$A=\int _0^{2}\left(x^{2}+2\right) d x+\int _2^{3}(2 x+2) d x$
$A=\frac{41}{3}$
$12 A=41 \times 4=164$
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