Chọn phương án A.

Phương trình hoành độ giao điểm:

• \(2x^2=0\Leftrightarrow x=0\).
• \(3-x=0\Leftrightarrow x=3\).
• \(2x^2=3-x\Leftrightarrow2x^2+x-3=0\)
  \(\Leftrightarrow\left[\begin{array}{l}x=1\\ x=-\dfrac{3}{2}.\end{array}\right.\)

Khi đó: $$\begin{aligned}S&=S_1+S_2\\
&=\displaystyle\int\limits_0^1\left|2x^2-0\right|\mathrm{\,d}x+\displaystyle\int\limits_1^3\left|3-x-0\right|\mathrm{\,d}x\\
&=\displaystyle\int\limits_0^12x^2\mathrm{\,d}x+\displaystyle\int\limits_1^3(3-x)\mathrm{\,d}x\\
&=\dfrac{2x^3}{3}\bigg|_0^1+\left(3x-\dfrac{x^2}{2}\right)\bigg|_1^3\\
&=\dfrac{2}{3}+2=\dfrac{8}{3}.\end{aligned}$$