A Treatise on the Integral Calculus: Containing the Integration of Explicit Functions of One Variable ; Together with the Theory of Definite Integrals and of Elliptic Functions

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J. & J.J. Deighton, 1844 - Calculus, Integral - 300 pages
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Page 207 - ... of the fixed stations be very small. Point out how, in a given position, to estimate the displacement caused by an error in the position of one of the fixed stations. 12. The tangents to the interior of two concentric and similar curves of the second order whose axes are coincident, cut off from the exterior curve equal areas. 13. A uniform rough cylinder is supported, with its axis horizontal, equally upon each of two elastic strings whose weights are inconsiderable ; the strings are equal in...
Page 198 - Oandx— 1) — 1.3.5 (2n-'l) w 2.4.6 ... 2'n~ ' 2' 12. Find the area of the curve traced out by the intersection of the sine of an arc, and the secant of half the arc, while the arc increases from 0 to a quadrant. 13. Shew that the number of primes is infinite.
Page 203 - Let abc (Fig. 19.) be a section of the pyramid made by a plane parallel to the base...
Page 190 - The surface of the same solid is £ (Зтг - 4) ira'. 15. The mean centre of the arc of a cycloid, from cusp to cusp, is at a distance *a from the base. 16. The mean centre of the area included between a cycloid and its base is at a distance £a from the base. 17. Prove...
Page 207 - To find the locus of the intersection of the tangent to a parabola and the perpendicular upon it from the vertex.
Page 117 - ... 2(— x . cos x + sin x) = x2 . sin x + 2x . cos x - 2 sin x.
Page 76 - Xp depend upon another of the same form, in which one of the indices is altered ; viz. that of л1 by the addition or subtraction of ra, and that of X by the addition or subtraction of unity.
Page 132 - ... and add the results together, and we shall obtain the same value for the definite integral...
Page 105 - ... the one of lower dimensions of the two expressions whose integrals are to be connected, and increasing each index by unity.

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