# Compute the volume of the solid formed by revolving

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18. Compute the volume of the solid formed by revolving the region bounded by 2 2 , 4 y x y x about (a) the x -axis; (b) y = 4.
20. Compute the volume of the solid formed by revolving the region bounded by 2 y x and 2 x y about (a) the y -axis; (b) x = 1.
26. Let R be the region bounded by 2 y x and y = 4 . Compute the volume of the solid formed by revolving R about the given line.
(a) y = 4 (b) the y -axis (c) y = 6 (d) y = –2 (e) x = 2 (f) x = –4 2 2 2 2 4 2 0 2 2 2 2 2 2 2 2 2 4 2 2 0 4 4 0 0 2 2 4 4 0 0 4 3 0 512 ) (4 ) 15 ) ( ) 8 384 ) ((6 ) 2) 5 1408 ) (6 (2 ) 15 ) ((2 ) (2 ) 16 128 8 3 3 ) 4 4 16 32 256 3 3 a v x dx b v y dy c v x dx d v x dx e v y y dy v ydy f v y y dy y v y 32. Suppose that the circle 2 2 1 x y is revolved about the y -axis. Show that the volume of the resulting solid is
4. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by , , y x y x   and