Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 297
y) of the curve. Hence Jpxds . fpjjds y fpds ff ds If p is assumed constant, it may be removed from under the integralsigns and canceled. The denominator of each fraction is then equalto s, a quarter circumference. To computethe numerators, we have, from the equationof the curve, ds = Vdx2 + df = -… … Ex. 2. Find the center of gravity of a quarter circumference of a circlewhen the amount of matter in a unit of length is proportional to the lengthof the arc measured from one extremity. As in Ex. 1, dm = pds, but here p = ks, k being a constant. Thendm = ksds. The integration is best performed by…
Geometry, Analytic · Calculus
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