Inverse Laplace transform of 1/s

1. Dec 16, 2016

influx

1. The problem statement, all variables and given/known data

2. Relevant equations
N/A

3. The attempt at a solution
The left hand side (red box) is the data sheet provided to us in the exam. The right hand side (blue box) is Wolfram Alpha. The data sheet says that the inverse Laplace transform of 1/s is equal to u(t) (i.e. the unit step) whereas Wolfram Alpha says that it is equal to 1. Which one is correct? Are they both correct? If so, how can that be since the unit inpulse, u(t), can take more than one value. For instance you can have u(t) =5? So shouldn't the data sheet also be 1 rather than u(t)?

Thanks

2. Dec 16, 2016

Staff: Mentor

u(t) is the unit step, not unit impulse.

Both are correct. You cannot have u(t) = 5, since the step size of a unit step is unity: 1. What you can do is scale the unit step by multiplying it by a constant. So you might have 5u(t) = 5, for t > 0.

The Wolfram result makes the implied assumption that the result applies for t > 0. That is, the result should be multiplied by a unit step: $1⋅u(t)$.