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

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SUMMARY

The discussion centers on the incorrect application of Laplace transforms in solving a differential equation. The user initially miscalculated the derivative u'(t) and mistakenly used a definite integral for v=2/s² instead of the required indefinite integral. This error led to the loss of time dependence in the solution, resulting in an incorrect answer. The clarification provided emphasizes the importance of correctly distinguishing between definite and indefinite integrals in the context of Laplace transforms.

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hyphagon
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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
 

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

Awesome, Thanks for for that. Makes sense now.
 

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