Volumes Of Solids Of Revolution

Let $f$ be a continuous function on $[a,b]$. Let $R$ be the plane region bounded by $f,y=0$ (thex-axis), $x=a$ (the vertical line at $x=a$), and $x=b$ (the vertical line at $x=b$). 

When it's revolved (rotated) about the x-axis, it generates a 3-dimensional space region. This 3-D space region is called a solid of revolution. Let's label it $S$. We wish to find its volume. Let $V$ be that volume.

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