#90 · Calculus · Improper integrals

Gabriel's horn

Revolve the curve $y = 1/ x$ for $x \geq 1$ around the $x$ -axis. The trumpet-shaped solid has a paradoxical property: a finite volume but an infinite surface area — you could fill it with paint but never paint it. Prove both facts.

~20 minWritten answer · compare with the solutionImproper integralsComparison testSurfaces of revolution

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