움직인 거리

$v ( t ) = - 3 \left( t + 2 \right) \left( t - 2 \right)$이고 $v \left( 2 \right) = 0$이므로 $\displaystyle \int _{0} ^{4} {\left| 12 - 3 t ^{2} \right| dt}$ $\displaystyle = \int _{0} ^{2} {\left. \left( 12 - 3 t ^{2} \right) dt \right.} + \int _{2} ^{4} {\left( - 12 + 3 t ^{2} \right) dt}$ $\displaystyle = \left[ \begin{array}{l} 12 t - t _{{} ^{}} ^{3} \begin{matrix} \\ \end{matrix} \end{array} \right] _{0} ^{2} + \left[ \begin{array}{l} - 12 t + t _{{} ^{}} ^{3} \begin{matrix} \\ \end{matrix} \end{array} \right] _{2} ^{4}$ $=$$16 + 32 =$$48$