Elements of mechanics: treated by means of the differential and integral calculus (1887)
Peck, William G[uy], 1820-1892. [from old catalog] · New York, Chicago, A. S. Barnes & company · leaf 79
coincide with thatof the area. We shall have, as before, z1 — 0. In thiscase, we have elm = ydx ; and, consequently, Formulas(32), reduce to fydx fydx (34.) Centre of Gravity of a parabolic area. 6§. Let A OB represent the area,having its chord at. right angles to theaxis. Let 0 be the origin of… … Fig. 43. y* = 2px .. y — Jlp . x .By substitution in the: first of Formulas (34), we have, . 3 2. /V 2p.x2dx f x2elx Xl = ~r- \ = ~T~fy2p .x2elx f x2elx CENTRE OF GRAVITY. 7* Integrating between the limits x = 0, and x = a, wehave, and, hence, J x3dx = |a , / a2d#o = *J «i = I «• That is, *Ae…
Mechanics
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