Definition 7.1.1 Laplace Transform
$f(t) = \begin{cases} \cos(t), & 0 \le t < \pi \\ 0, & t \ge \pi \end{cases}$
Complete the integral(s) that defines $\mathcal{L}\{f(t)\}$.
$\mathcal{L}\{f(t)\} = \int_0^{\pi} (\text{________}) dt + \int_{\pi}^{\infty} (\text{________}) dt$
Find $\mathcal{L}\{f(t)\}$. (Write your answer as a function of $s$.)
$\mathcal{L}\{f(t)\} = \text{________} \quad (s > 0)$
