Abstract
This chapter discusses a large class of integrable functions, which includes most functions of frequent occurrence in practice. The function f is called admissible only if f is bounded, f has bounded support, and f is continuous except on a negligible set. The properties of step functions are easily established, and an arbitrary function is integrable only if it is closely approximated by step functions. Two applications of Fubini's theorem are the generalizations of methods used in elementary calculus courses, either to define or to calculate volumes. In integration problems, which display a cylindrical or spherical symmetry, the use of polar or spherical coordinates is clearly indicated. A related application of multiple integrals is to the computation of force. A force field is a vector-valued function. In writing multidimensional integrals with differential notation, the order of the differentials in the integrand makes a difference.
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