Answer
$W_{L} = 0 J \ \ \ \ \ \ -\infty10$
Work Step by Step
The energy of the inductor is the integration of the power across the inductor
$W = \int {P_L\ dt} = \int {i(t)\times v_L(t)\ dt}= \int{ L\times i\times \frac{di}{dt}} \ dt$
for $=\infty 10$
$W =2* \int^0_{-\infty} {0\ dt} +2 \int^{10}_{0} {t \ dt} + 2 \int^{t}_{10} {0\ dt}= t^2 |^{10}_0$
$ = 100 J, \ \ \ \ \ \ \ \ t>10$
