1. Examples: Construct examples of the thing(s) described in the following. (a) A region that, when revolved around the x-axis, has both disk and washer cross sections. (b) A region that, when revolved around the y-axis, has both disk and washer cross sections. (c) A solid of revolution for which it is not possible to use the disk or washer method. 2. Consider the rectangle bounded by y = 3 and y = 0 on the x-interval [2, 2.25]. (a) What is the volume of the disk obtained by rotating this rectangle around the x-axis? (b) What is the volume of the washer obtained by rotating this rectangle around the line y = 5? 3. Each of the definite integrals in Exercises 19 24 represents the volume of a solid of revolution obtained by rotating a region around either the x- or y-axis. Sketch this region. (a) * (16 - (x + 1)2)de (b) * / sin? (x)de (c) * (x2 - 2x + 1 )de 2 (d) nydy4. Write the volume of the two solids of revolution that follow in terms of definite integrals that represent accumulations of disks and/or washers. Do not compute the integrals. a) y = f(x) b) y y = f ( x) 3+ 2- - X -1- -3 -2+ 5. Consider the region between the graphs of f(x) = 5 - xand g(x) = 2x on [1, 4). For each line of rotation given in find a definite integral which computes the volume of the resulting solid. Do not compute the integral. Around the x-axis Around the line x = 1 a) y b -x