Hello, Im currently revising for my university maths exam and have found the following question:

F(s) denotes the laplace transform of the causal signal f(t), with the region of convergence Re(s) >σc. Prove the first shift theorem, using the basic definition of the laplace transform, by showing that the transform of e^at f(t) is given by L{f(t)}=F(s-a), with the region of conversion Re(s)>σc +Re(a).

Im not really sure what its asking. I know that the first shift theorem is:

L{e^at f(t)}=F(s-a), where F(s)=L{f(t)}

and i know that the definition of a laplace transform is:

F(s)=L{f(t)}=¦(meaning integral from 0- infinity in this case)of e^-st f(t) dt.

How do i use these to come up with the answer that is expected? In the question, this is worth 5 marks out of a total 20.

All help appreciated, Thank you.

Andy