Let the area of the region (x,y):0 x 3,0 y minx^2+2,2x+2 be A.

Question

Let the area of the region ${(x,y):0\le x\le 3,0\le y\le min{{x}^{2}+2,2x+2}}$ be A. Then $12A$ is equal to \_\_\_\_\_\_\_\_\_\_.

Answer: 164

Accepted Answer

$\begin{gathered} y=2x+2 \ A=\int _{0}^{2}({x}^{2}+2)dx+\int _{2}^{3}(2x+2)dx \ A=\frac{41}{3} \ 12A=41	imes 4=164 \end{gathered}$

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