A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 336
^xdxand read, the integral of dy equals the integral of .^ ~-_^, which equals (1 — X2)2 1—X^ Ix (1 —x2)2 1—X^ The conception of integration as a process having forits object the summation of an infinite series of infinites-imals may be illustrated by considering the area of anellipse as composed of… … DEFINITIONS AND ELEMENTABY FOKMS. 103 Now it is found that dA = -{a^ — x^^) dx. By integration it is found that the entire area is Ttah, h and 6 being the semi-axes. But, as the entire area is the sumof the infinitesimal segments, the process of integration may be considered ashaving for its object…
Geometry, Analytic · Calculus
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