Answer
$180$ $J$
Work Step by Step
The work is calculated with the formula:
$W$ = $\int_a^b{F(x)}dx$
The force function is given by $F(x)$ (in newtons) and the work (in joules) is the area under the curve, given by
$$\begin{align*}
\int_0^8{F(x)}dx& = \int_0^4{F(x)}dx + \int_4^8{F(x)}dx \\
&= \frac{1}{2}(4)(30)+(4)(30)\\
& = 180 J
\end{align*}$$