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Home Applications of the Integral Volumes of Solids of Revolution Region between Two Curves  
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Region Between Two Curves  Solid of Revolution
Now we consider the region R between two curves y = f(x) and y = g(x) from x = a to x = b. Rotating R about the xaxis generates a solid of revolution S shown in Figure 6.2.6(c). Figure 6.2.6 (a): R_{2}, S_{2} Figure 6.2.6 (b): R_{1}, S_{1}
Figure 6.2.6 (c) R = R_{2}  R_{1}, S = S_{2}  S_{1} Let R_{1} be the region under the curve y = f(x) shown in Figure 6.2.6(b), and R_{2}, the region under the curve y = g(x), shown in Figure 6.2.6(a). Then S can be found by removing the solid of revolution S_{2} generated by R_{1} from the solid of revolution S_{2 }generated by R_{2}. Therefore volume of S = volume of S_{2}  volume of S_{1}. This justifies the formula We combine this into a single integral. VOLUME BY DISC METHOD Another way to see this formula is to divide the solid into annular discs (washers) with inner radius f(x) and outer radius g(x), as illustrated in Figure 6.2.7. Figure 6.2.7


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