i(t)=\dfrac{w(t)}{v(t)}=\dfrac{w(t)}{12}
\displaystyle\int_{0}^{14} i(t)dt=\dfrac{1}{12}\Bigl[\displaystyle\int_{0}^{3} 2tdt +\displaystyle\int_{3}^{4} 6dt +\displaystyle\int_{4}^{6} (18-3t)dt +\displaystyle\int_{6}^{8} 0dt +\displaystyle\int_{8}^{10} (8-t)dt +\displaystyle\int_{10}^{12} (-2)dt +\displaystyle\int_{12}^{14} (t-14)dt\Bigr]
=\dfrac{13}{12}(C)