O i b b o i a a r x r x r dx r dx v x dx x dx v x dx

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(4 ) 4 4 4 4 8 16 8 16 8 16 5 3 5 8 16 5 3 5 o i b b o i a a r x r x r dx r dx V x dx x dx V x dx x dx x x dx x x x dx x dx dx x C x x dx x dx C x x x V x 2 2 32 64 32 64 32 32 32 32 5 3 5 3 5 5 512 64 320 64 15 5 15 3 V V 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 a. b. WA 1, p. 7 , 4 4 8 1 6 2 5 6 2 5 6 5 1 2 8 1 6 5 1 5 1 5 1 5 V r d x r x V x d x x x d x x x V x x
c. d. 2 2 0 2 2 2 2 2 2 2 2 2 4 2 2 2 2 5 3 15 15 2 2 2 4 ( 2) 6, ( 2) 2 6 2 36 4 4 4 376 376 36 4 72 72 5 3 15 15 2160 752 1408 15 15 15 i r r x x V dx x dx V dx x x dx x x V x x V     e. WA 1, p. 8 2 2 2 2 2 2 2 2 2 2 42 2 2 2 53 2 2 2 6 ,642 62 12364 12 364 53 232232384 88 55 5 o i rxr Vxdxdx Vxxd xd x xx Vxx V                          3 3 2 2 4 4 2 2 0 0 4 4 0 0 4 4 2 2 0 2 , 2 (2 ) (2 ) 4 4 ( 4 4) 8 8 4 4 2 3 2 3 136 8 128 3 3 3 o i o r yr y V ydy ydy V y y dy y y dy y y y y V y y V                        
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

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