Problem $1$

$1$a$)40$ points: Find the Laplace transform $L\{sin(t)u(t)\}$ by using the knowledge that

$L\{cos(t)u(t)\}=\frac{s}{s^2+1}$

Problem $2$

A signal is described mathematically by:

$x(t)=tu(t)-2(t-1)u(t-1)+(t-2)u(t-2)$

$2$a$)10$ points: Represent this signal graphically.

$2$b$)20$ points: Find the Laplace transform $x(s).$