 | Francis Bashforth - 1873 - 410 pages
...д. ДХ-; 'и ,+ Д'"-'I х-3' + ^Х-и 4ДХ^4 + A«xJ. + ДЧ.1. be integrated In the ordinОry way. Suppose yx to be the ordinate of a curve corresponding...area bounded by the curve, the axis of x, and the ordinales at the distances a and a + ?, will be equal to °j°íl¡/xdx = y'y.„|rfn/ = y/y.^jrf?1... | |
 | Benjamin Osgood Peirce - 1888 - 200 pages
...intensity, when Q is at that point, of the component parallel to KL of the force between M and M', the area bounded by the curve, the axis of x, and the ordinates at K and L will be numerically equal to the work done in moving M' from the one position to the other.... | |
 | Walter William Rouse Ball - 1889 - 292 pages
...Al ;!> XT' 3TJ 'BU He next considered curves of the form y = x™ and established the theorem that the area bounded by the curve, the axis of x, and the ordinate x=\, is to the area of the rectangle on the same base and of the same altitude as m : m +... | |
 | Walter William Rouse Ball - 1901 - 586 pages
...i , 3'ff, TJff, Ac. He next considers curves of the form y = x "* and establishes the theorem that the area bounded by the curve, the axis of x, and the ordinate x--l, is to the area of the rectangle on the same base and of the same altitude as m : m +... | |
 | William Anthony Granville - 1911 - 492 pages
...limits OA = a and OB = 6), .. . '' limit Hence the volume generated by revolving, about the axis of J", the area bounded by the curve, the axis of X, and the ordinates z = a and z = 6 is given by the formula where the value of y in terms of z must be substituted from... | |
 | Leonard Berger Benny - 1927 - 512 pages
...co-ordinates are (x+Ax, y+Ay), so that the width P'Q' of the strip PP'Q'Q is Ax. Let aAx represent the area bounded by the curve, the axis of x, and the ordinates AA', PI3', ie the area AA'P'P. If x increases to x + Ax, PP' moves to QQ'. Hence, if aAx= AA'P'P, we... | |
 | Henry Lewis Rietz - 1924 - 242 pages
...integral, A = I f(x)dx, represents the area under the curve y = f(x) from * = a to x = 6 (that is, the area bounded by the curve, the axis of x, and the ordinates corresponding to x = a and x = b; any area below the axis being taken as negative). The problem of... | |
 | Kenneth A. Ross - 2014 - 192 pages
...There is no constant to be added since S is zero when x is zero. Next take the curve y = 2x — a?. The area bounded by the curve, the axis of x and the ordinate PN is seen to be ~ x2 There is again no constant to be added since the area and x vanish together.... | |
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... is to the area of the rectangle on the same base and of the same altitude as m : m + 1. This is equifl valent to finding the value of I xmdx. 