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EXAMPLE 1Using the Disk Method: Revolving About the x-Axis

Find the volume of the solid of revolution generated by revolving the region bounded by the graph of y=x, the x-axis, and the line x=5 about the x-axis.

Solution We begin by graphing the region to be revolved. See Figure 16(a). Figure 16(b) shows a typical disk and Figure 16(c) shows the solid of revolution. Using the disk method, the volume V of the solid of revolution is V=π50(x)2 dx=π50x dx=π[x22]50=252π cubic units