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Unformatted text preview: write: 3 3 1 3 1 3 1 2 = = = = âˆ« x dx x V . Notice that we got the volume of the shape to be h r 2 3 1 , which happens to be the equation for volume of a cone. A solid of revolution is one generated by rotating a plane region a out a line that lies in the same plane as the region. For example, if the line 3 = y , 4 2 â‰¤ â‰¤ x , is rotated about the xaxis, what solid is formed? 3 = y 2 4 ( 29 18 2 9 ) 2 4 ( 9 9 9 3 ) ( 4 2 4 2 4 2 4 2 4 2 2 2 = Ã— == = = = = = âˆ« âˆ« âˆ« âˆ« x dx dx dx y dx x A V Ex . Write the integral for the volume of the plane region defined by the function r y = from x=a to x=b Ex . Find the volume of the solid obtained by rotating about the xaxis the region under the curve x y = from 0 to 1. Assign: p.456 #1, 7, 9, 13, 27, 29...
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This note was uploaded on 07/12/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Kim
 Calculus, Cone

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