00:01
Hi there, so for this problem, we need to find the laplace transform of a times t plus one, then this times u of t minus one.
00:14
Okay, so we need to find this laplace transform.
00:17
So in this case, what we are dealing in here is with a this function here, which is named as the unit step function.
00:30
Okay.
00:33
So then the first step that we are going to do to solve this problem is to use the shifting theorem.
00:40
So the shifting theorem will be that the laplace transform a sum function f of t times u, the step function, available at t minus a, will be the s penumptial of minus a times s times the loplas transform of the function.
01:04
T plus a.
01:08
Okay, you can recognize that in our case, comparing with this expression, a is one, and the function f of d will be then a times t plus one.
01:24
So first, let's find, so what we are going to do first is remember that then, well, using this formula in here, we will have that this then, it will be the exponential of minus s, okay, because a is one, this times the lo -plus transform of the function f, evaluated at t plus 1...