32 64 32 32 32 5 3 5 5 64 15 5 15 3 V WA 1 p 4 b same region rotated

# 32 64 32 32 32 5 3 5 5 64 15 5 15 3 v wa 1 p 4 b same

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32 64 32 32 32 5 3 5 5 512 64 320 64 15 5 15 3 V WA 1, p. 4
b. same region rotated around y=4 will be the same volume as the region rotated around the x -axis. WA 1, p. 5
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 5 3 4 2 5 2 2 4 2 5 3 5 2 4 4 (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. a. b. WA 1, p. 6 , 2 5 1 1 3 0 0 2 5 1 0 y x x y r y r y V r d y r d y V y d y y d y y y V y d y y d y V 3 2 2 2 2 2 2 1 1 2 1 1 4 2 1 1 5 3 2 0 0 1 , 1 1 1 2 1 2 1 2 4 5 3 2 3 8 1 11 0 0 15 6 30 i o b b o i a a o o o o r y r y V r dy r dy V y dy y dy V y y dy y y dy y y y y V y y V