Conceptual understanding of disk and shell method: a Write...

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MA 114 Worksheet #12: Volumes of Revolution (Shell Method) 1. Conceptual understanding of disk and shell method: (a) Write a general integral to compute the volume of a solid obtained by rotating the region under y = f ( x ) over the interval [ a, b ] about the y -axis using the method of cylindrical shells. (b) If you use the disk method to compute the same volume, are you integrating with respect to x or y ? Why? 2. Sketch the enclosed region and use the Shell Method to calculate the volume of rotation about the y -axis. (a) y = 3 x - 2, y = 6 - x , x = 0 (b) y = x 2 , y = 8 - x 2 , x = 0, for x 0 3. Sketch the enclosed region and use the Shell Method to calculate the volume of the solid when rotated about the x -axis. (a) x = 1 4 y + 1, x = 3 - 1 4 y , y = 0 (b) x = y (4 - y ), x = 0 4. Use both the Shell and Disk Methods to calculate the volume obtained by rotating the region under

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