Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 4 / 14A / a / Solution

For $a>0$, the Heaviside step function vanishes before $a$ and is one afterwards. For $\mathrm{Re}p>0$,The value assigned at the single jump point does not affect this Laplace transform. The positive real part ensures convergence at infinity.