Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. Sketch the region and a typical shell.

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15. y x, y = 0, x = 1, x= 2: about x = 1 16. y = x, y = 0, x= -2, x = -1: about the y-axis 17. y = x, y = 0, x= 1, x= 2: about x = 4 18. y 4x – x, y = 8x – 2r: about x = -2 19. y = x - 1. y = 0, x 5: about y = 3 20. y = x, x = y*; about y = -1