Answer
$0$
Work Step by Step
The work is calculated with the formula:
$W$ = $\int_a^b{f(x)}dx$
$$\begin{align*}
W&=\int_1^{1.5}{\cos\frac{\pi{x}}{3}}dx+\int_{1.5}^{2}{\cos\frac{\pi{x}}{3}}dx\\
&= \left[\frac{3}{\pi}\sin\frac{\pi{x}}{3}\right]_1^{1.5}+\left[\frac{3}{\pi}\sin\frac{\pi{x}}{3}\right]_{1.5}^{2}\\
&= \frac{3}{\pi}\left[\sin\frac{\pi}{2}-\sin\frac{\pi}{3}\right] + \frac{3}{\pi}\left[\sin\frac{{2}\pi}{3}-\sin\frac{\pi}{2}\right]\\
&= \frac{3}{\pi}\left(1-\frac{\sqrt 3}{2}\right) + \frac{3}{\pi}\left(\frac{\sqrt 3}{2}-1\right)\\
&= 0.
\end{align*}$$
