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 190
——\- G, or G= — ^r=-. The cor- A iCL A id reded integral is therefore z = ^——[(1 -\- ^ax) — 1]. Aid To illustrate this result consider A M the curve whose lengthis to be found, or, which is to be rectified. As this curveis infinite in extent, we can inquire only for the length ofsome specified… … Fig. 173. it required to find the length of some other arc, as PP, we should integrate between the limits .r = AD, and ic = AD. Thus, let AD = 6 and AD = c. 8 ^ Besuming the indefinite or general integral z = ^-{1 + ^ax)^ -\- C, substituting A (CL successively x = h, and x= c, and subtracting the…
Geometry, Analytic · Calculus
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