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Unformatted text preview: y = x and y = √ x about the line y = 1. Be sure to sketch the region. Solution: Volume = π Z 1 • (1x ) 2(1√ x ) 2 ‚ dx = π 6 . Quiz for Thursday, October 14 1. Use slices to ﬁnd the volume of the solid obtained by rotating the region bounded by y = x,y = 0 ,x = 2 , and x = 4 about the line x = 1. Be sure to sketch the region. Solution: Volume = π Z 2 (91) dy + π Z 4 2 ( 9( y1) 2 ) dy = 25 1 3 π. 2. Use shells to ﬁnd the volume of the solid obtained by rotating the region bounded by x = 4 y 2y 3 and x = 0 about the xaxis. Be sure to sketch the region. Solution: Volume = 2 π Z 4 y (4 y 2y 3 ) dy = 512 5 π....
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This note was uploaded on 04/29/2010 for the course MATH 31B 31B taught by Professor Liggett during the Spring '10 term at UCLA.
 Spring '10
 liggett

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