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S OLIDS OF R EVOLUTION 4-G

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Disk method

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Find Volume – Disk Method Revolve about a horizontal axis Slice perpendicular to axis – slices vertical Integrate in terms of x Revolve about a vertical axis Slice perpendicular to axis – slices horizontal Integrate in terms of y

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Washer Method

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Volume of Washer: Horizontal axis of revolution Slice with rectangle perpendicular to axis Integrate in terms of x Vertical axis of revolution Slice with rectangles perpendicular to axis Integrate in terms of y Find Volume – Washer Method

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1) Find the volume of the solid is bounded by the curve y = x and the x-axis between x = 0 and x = 1 rotated about the x-axis

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2)Find the volume of the solid when the region bounded by is revolved about the x-axis

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3) Find the volume of the solid generated when the region bounded by is revolved about the x-axis

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4) Find the volume of the solid generated when the region bounded by is revolved about the line y = 4

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5) Set up the integrals for finding the volume of the solid formed by revolving the region formed by a) About the x-axisb) about y = -1

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6) Find the volume of the solid generated when the region bounded by is revolved about the line y = 3

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7) Find the volume of the solid generated when the region bounded by is revolved about the y-axis

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H OME W ORK Finding Volumes of solids using washers and disks worksheet

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