00:01
In this problem, we are given this function f of t equal to integral from 0 to t, tau, sine, tau, d tau.
00:14
And using the properties of the laplace transform, we are going to compute the laplace transform of this function.
00:23
Okay, now, if we call this function, g of tau, then the first property that we, are going to use is the laplace transform of an integral.
00:43
So if we have this integral from 0 to t, and if we have this function, then we have the laplace transform of g of t divided by s.
00:56
So now we need to compute the laplace transform of this function.
01:02
So we have g of t equal to t times sine t.
01:07
Again, we have this form t times.
01:11
Something so we know how to take the laplace transform using the properties so if we if we call this function h of t then the laplace transform of this function is okay this is t to the power 1 have minus 1 to the power 1 this number d over ds the first derivative again because of this power and we have the laplace transform of h of t.
01:51
So the laplace, the first laplace transform that we compute is this one and this is the only laplace transform that we compute...