Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 289
a-h. APPLICATIONS OP INTEGRATION 131. Length of a plane curve. To find the length of anycurve AB (fig. 174), assume n — 1 points, //, 7f, • • •, %_v be-tween A and /. and connect each pair of consecutive points bya straight line. The length of AB isthen defined as the limit of the sumof the lengths… … Fig. 174 d8 = Vda?+dtf in Cartesian coordinates, and in polar coordinates.Hence we have and ds = ^dr+r\W> 8=fV,h*+d!f 8= fy/d)*+i*dff\ CO (2)(3)(4) To evaluate either (3) or (4) we must express one of thevariables involved in terms of the other, or both in terms of athird. The limits of…
Geometry, Analytic · Calculus
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