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Section 7.3 Volume by shells
Objectives
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Compute volume by adding the contributions of thin cylindrical shells.
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Use shell height and radius to quantify each shell’s contribution.
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Choose shells or washers based on which method aligns with the region’s geometry.
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Start with an example that can’t be done with washers because of non-invertible functions.
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If the region under the curve \(y=f(x)\) from \(a\) to \(b\) (\(0\le a \lt b\)) is revolved around the \(x\)-axis, the volume is
\begin{equation*}
V=\int_{a}^{b} 2\pii xf(x)\dd{x}
\end{equation*}
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Include something about how to know which method may be best.
