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We construct an infinitely tall wizard hat .S as follows. Let R be the region enclosed between the curve y = % and x =

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We construct an infinitely tall wizard hat .S as follows. Let R be the region enclosed between the curve y = % and x = 0 on the unbounded interval y > 1. The wizard hat .S is obtained by rotating R about the y-axis. Does the wizard hat .S have a finite volume

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