Part $2$: By using the Laplace transform, compute the convolution $x(t)**v(t)$ where:

a$)x(t)=e^{-t}u(t),v(t)=sin(t)u(t)$

b$)x(t)=si{n}^2(t)u(t),v(t)=(t)$

Note: $si{n}^2(t)$ cam be written as:

$si{n}^2(t)=\frac{1-cos(2t)}{2}$

Solve $a$ &$b$ step $by$ step