Equivalence of the washer and shell methods for finding
Chapter 6, Problem 45E(choose chapter or problem)
Equivalence of the washer and shell methods for finding volume Let ƒ be differentiable and increasing on the interval a? x? b, with a > 0, and suppose that ƒ has a differentiable inverse f-1. Revolve about the y-axis the region bounded by the graph of ƒ and the lines x=a and y=f(b) to generate a solid. Then the values of the integrals given by the washer and shell methods for the volume have identical values:
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