Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 455
integration are illustrated in I ii n a the following examples: Ex. 1. Required the curve the slope of whichat auy point is twice the abscissa of the point. By hypothesis, — = 2 x.ax Therefore y = x% + C. (1) Any curve whose equation can be derivedfrom (1) by giving C a definite value satisfiesthe… … Fig. 238 But if it is required that the curve should pass through (—3, 10), wehave, from (1), 10 = 9 + C; whence C = l, and the equation is y = x2 + 1. 438 EXAMPLES 439 Ex. 2. Required a curve such that the length of the tangent from anypoint to its intersection with OF is constant. Let P(x, y)…
Geometry, Analytic · Calculus
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