7.1: Introduction to the Laplace Transform - Mathematics LibreTexts
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webJul 16, 2020 · Definition of the Laplace Transform. To define the Laplace transform, we first recall the definition of an improper integral. If \(g\) is integrable over the interval \([a,T]\) for every \(T>a\), then the improper integral of \(g\) over \([a,\infty)\) is defined as \[\label{eq:8.1.1} \int^\infty_a g(t)\,dt=\lim_{T\to\infty}\int^T_a g(t)\,dt.\]
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