When I read Steve's article (see page 18), I saw that there was an alternate strategy for integrating piecewise functions in Mathematica. Electrical engineers in particular will say, "Why not use Laplace or Fourier transforms?" Using Laplace transforms to manipulate piecewise functions has been a technique known since the days of Heaviside in the nineteenth century. A unified theory for all transforms had to await the 1950's and Schwarz's theory of distributions (not to be confused with probability distributions) and generalized functions.
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