Answer
$0$
Work Step by Step
In order to compute the work, we will use the following formula:
$\int_C F \ dt=\int_a^{b} [F[r_1(t)] r_1'(t) \ dt +\int_c^{d} F[r_2(t)] r_2'(t)] \ dt$
The parametrisation of the curve are: $r_1(t)= \lt 0, t, 0 \gt \implies r_1'(t) = \lt 0, 1, 0\gt$ and $r_2(t)= \lt 0, 1, 4t \gt \implies r_2'(t) = \lt 0, 0, 4\gt$
Now, $\int_C F \ dt=\int_a^{b} [F[r_1(t)] r_1'(t) \ dt +\int_c^{d} F[r_2(t)] r_2'(t)] \ dt\\=\int_0^{1} \lt -t, 0, 0\gt \cdot \lt 0, 1, 0 \gt \ dt+\int_0^{1} \lt -1, 4t, 0\gt \cdot \lt 0, 0, 4 \gt \ dt \\=\int_0^1 0 \ dt+\int_0^1 0 \ dt\\=0$
