MATH116 Lecture Notes - Lecture 15: Tvr2, Crass
9 Dec 2015
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Friday, november 27 lecture 33 : volumes of a solid of revolution: disks method. Expectations: determine the volume of a solid of revolution generated by revolving a region about an axis, by using the disk method. 33. 1 introduction in this lecture we study methods for determining the volume of some simple solids for which we can obtain a formula for its cross-sections. 33. 2 the principle behind the cross section method. Suppose we are given a solid s lying alongside, skewed by the x-axis, whose extremities are given by the planes x = a and y = b, in 3-space. Let us subdivide the interval [a, b] into n equal subintervals a = x0, x1, x2, , xn 1, xn. = b, each of length x = (b a) / n. Thus a(x1), a(x2), , a(xn) represent a sequence of areas of cross sections of the solid s at x1, x2, , xn-1, xn .
