Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 286
r planes p so that the ends of its axes are on the two given ellipses, the plane of the moving ellipse being per- pendicular to those of the given ellipses. Required the volume of the solid generated. Let the given ellipses be ABAW (fig. 169) with semiaxes OA =a and OB = b, ami ACAC with semiaxes… … 169 270 APPLICATIONS OF INTEGRATION But from the ellipse ABAB -n + ^f- = 1 a2 lr and from the ellipse ACAC - + J—^- = 1 be PM -PN = -(a2- x2).a2 Therefore Consequently the required volume is —— (a2 — x2) dx = - Trdbc.■ a a- o The solid is called an ellipsoid (§ 143, Ex. 5). Ex. 2. The axes of two…
Geometry, Analytic · Calculus
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