In the question I posted, he asked me to take Laplace in part (ii), and I posted both the question and the solution. He used double integral in his solution, but I could not fully understand what he did. Can you explain it more clearly step by step?

Question 1. (a) Let f(t) be a function with Laplace transform F(s). Find Laplace trans- forms of: .t (ii) g(t) = / f(t') at'ii. g(t) = / f(t') dt' 0 OO L(g(t) ) = f(t') dt') e- st dt = f(t')e-st dt dt' -OJt=t' dt) dt' = 1 (t)(be-stat G S = -F(s) S