Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. x = 4y - y², x = 0 64/3 ? 32/3 ? 256/3 ? 128/3 ?
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The region is bounded by the curve \( x = 4y - y^2 \) and the line \( x = 0 \). To find the bounds in \( y \), we solve \( 4y - y^2 = 0 \): \[ y(4 - y) = 0 \implies y = 0 \text{ or } y = 4 \] Thus, the region is between \( y = 0 \) and \( y = 4 \). Show more…
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