(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.
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
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