Chapter 6 | Applications of Integration
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Figure 6.18 (a) A thin rectangle for approximating the area under a curve. (b) A representative disk formed by revolving the rectangle about the x -axis. (c) The region under the curve is revolved about the x -axis, resulting in (d) the solid of revolution.
We already used the formal Riemann sum development of the volume formula when we developed the slicing method. We know that V = ∫ a b A ( x ) dx . The only difference with the disk method is that we know the formula for the cross-sectional area ahead of time; it is the area of a circle. This gives the following rule.
Rule: The Disk Method Let f ( x ) be continuous and nonnegative. Define R as the region bounded above by the graph of f ( x ), below by the
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