L38 Volumes Shell - L38 Volume of Solid of Revolution II{...

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Unformatted text preview: L38 Volume of Solid of Revolution II{ Shell Method Shell Method is another way to calculate the volume of a solid of revolution when the slice is parallel to the axis of revolution and you integrate perpendicular to the axis of revolution. V shell = 2 rhdx = 2 (shell-radius)(shell-height) dx 1 The necessary equation for calculating such a volume depends on which axis is serving as the axis of revolution. V ver = Z A ( x ) dx if the rotation is around a vertical axis of revolution. V hor = Z A ( y ) dy if the rotation is around a horizontal axis of revolu- tion; Note: A shell = 2 (shell-radius)(shell-height) 2 ex. Determine the volume of the solid obtained by rotating the region bounded by y = ( x 1)( x 3) 2 and the x axis about the y-axis. ( 24 5 ) 3 ex. Determine the volume of the solid obtained by rotating the region bounded by y = x 2 + x and y = 0 about the line y axis. ( 6 ) 4 The remaining examples will have axis of rotation about axis other than the x , and y axis: ex. Determine the volume of the solid obtained by rotating the region bounded by x = ( y 2) 2 and y = x about the line y = 1. ( 63 2 ) 5 ex.ex....
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L38 Volumes Shell - L38 Volume of Solid of Revolution II{...

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