### Second Shift Formula for a Piecewise-defined Function

ODEs: Find the Laplace transform of the piecewise-defined function f(t) = t on (0,1), 1 on (1,3) , and 4-t on (3,4). We proceed by rewriting f(t) in terms of shifted unit step functions and then apply the Second Shift Formula. We check our work using integration by parts.

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