15 - Disk

# 15 - Disk - b x = 1 c the y-axis d y =-1 e y = 2 f x =-1 Do...

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Volumes of Solids of Revolution The volume of a slice is the area of the slice multiplied by the width of the slice. v i ±=±(area of side of slice i )(width i ). The total volume will then be: v A ± dw a b . We are going to examine slice perpendicular to the axis of revolution. When we revolve the slices, we get disks or washers depending on the initial region. (On the quizzes, this may be referred to as using planar slices.)

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Ex. Find the volume of the solid generated by revolving the region bounded by y x 2 3 , the x-axis, and x = 1 around: a. the x-axis

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Unformatted text preview: b. x = 1 c. the y-axis d. y = -1 e. y = 2 f. x = -1 Do: 1. Let R be the region in the xy plane bounded by y 4 x ,± x 2,±and± y 1 4 . Set up the integral for the volume of the solid obtained by rotating R about the y-axis, using planar slices perpendicular to the axis of rotation. 2. Let R be the region in the xy plane bounded by y 2 x 2 ±and± y 3 x-1 . Set up the integral for the volume of the solid obtained by rotating R about the x-axis, using planar slices perpendicular to the axis of rotation....
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15 - Disk - b x = 1 c the y-axis d y =-1 e y = 2 f x =-1 Do...

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