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On the Nature of the Calculus Swoosh

1) Introduction
The Riemann integral is the definite integral normally encountered in calculus texts and used by physicists and engineers. Other types of integrals exist (e.g., the Lebesgue integral), but are unlikely to be encountered outside the confines of advanced mathematics texts. The Riemann integral is based on the Jordan measure, and defined by taking a limit of a Riemann sum.

2) Notation
The standard notation for Riemann's integral is the "calculus swoosh" . Two disadvantages of this notation are that the calculus swoosh takes two lines, and when evaluating integrals, one can use two to four times as much paper as for any other computation. Thus utilizing sigma form is deemed a perfectly valid alternative. [1]

[1] Anonymous, 2021

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