Why can't I substitute a Laplace transform into an integration?

[hyphagon]

Hi, I was given the attached question and have given my wrong attempt at the answer. I know how to work the answer out (also shown) but I would like to know why my first attempt is wrong.

Many Thanks

 

[vela]

First, you calculated u'(t) incorrectly. Second, when you said v=2/s², you used the definite integral of dv/dt. You need to use the indefinite integral. You can't get rid of the t dependence.

 

[hyphagon]

Yup, I integrated it by mistake. That now makes it equal zero incidentally.

Awesome, Thanks for for that. Makes sense now.