An Elementary Treatise on the Integral Calculus: Founded on the Method of Rates or Fluxions (Classic Reprint)

This work, as at present issued, is designed as a shorter course in the Integral Calculus, to accompany the abridged edition of the treatise on theD ifferential Calculus, by Professor J. Minot Rice and the writer. It is intended hereafter to publish a volume commensurate with the full edition of the work above mentioned, of which the present shall form a part, but which shall contain a fuller treatment of many of the subjects here treated, including Definite I ntegrals, and theM echanical Applications of the Calculus, as well as Elliptic I ntegrals, Differential Equations, and the subjects of Probabilities and A verages. The conception of Rates has been employed as the foundation of the definitions, and of the whole subject of the integration of known functions. The connection between integration, as thus defined, and the process of summation, is established inS ection VII. Both of these views of an integral namely, as a quantity generated at a given rate, and as the limit of a sum have been freely used in expressing geometrical and physical quantities in the integral form.
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