Abstract
AbstractIn Chap. 6 we discuss the improper and dominated integrals; in particular, the latter addresses the question as to when a function is majorized by a positive steadily decreasing function with a convergent improper integral. We also explore the relation between uniform and improper integrals and note the simplicity of computation when dealing with uniform integrals. Quadrature rules converge to the integral of the function when the function is Riemann integrable, but in the case of the improper Riemann integral, this connection is obscured by the double limiting process involved. The dominated integral, which is defined by a single limit, allows for this connection.
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