Ta có:

$\frac{dL}{dt}=v\left( t \right)={{2.10}^{3}}{{e}^{-t}}t\Rightarrow L\left( x \right)-L\left( 0 \right)$$=\int_{0}^{x}{{{2.10}^{3}}{{e}^{-t}}tdt}$

$\begin{align}  & \Rightarrow L\left( x \right)=L\left( 0 \right)-{{2.10}^{3}}\left( \left. \left( t{{e}^{-t}} \right) \right|_{0}^{x}-\int_{0}^{x}{{{e}^{-t}}dt} \right) \\  & \Rightarrow L\left( x \right)=L\left( 0 \right)-{{2.10}^{3}}\left( x{{e}^{-x}}-\left. \left( -{{e}^{-t}} \right) \right|_{0}^{x} \right) \\ \end{align}$

$\begin{align}  & \Rightarrow L\left( x \right)=L\left( 0 \right)-{{2.10}^{3}}\left( x{{e}^{-x}}+{{e}^{-x}}-1 \right) \\  & x=20;L\left( 0 \right)=17\Rightarrow L\left( 20 \right)=2017 \\ \end{align}$

Vậy đáp án đúng là A.