More Volumes of Solids of Revolution
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More Volumes of Solids of Revolution

[From: ] [author: ] [Date: 12-07-04] [Hit: ]
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(2) Sketch the region enclosed by the graph of y = 2x-x^2 and the x-axis nd the volume of the solid
produced when that region is revolved about the y-axis.

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Since we are revolving about the y-axis we will use cylindrical shell method and integrate with respect to x.

y = 2x − x² intersects x-axis at 0 and 2, so we integrate from 0 to 2

Each cylindrical shell has:
radius = x
height = 2x − x²

V = 2π ∫₀² x(2x− x²) dx = 8π/3
1
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