We are all familiar with Gabriel's Horn, where the function f(x) = 1/x generates an infinite area but a finite volume when revolved around the x-axis.(adsbygoogle = window.adsbygoogle || []).push({});

So the other day I stumbled upon a particular interesting integral: ∫ from 0 to 1 1/x^{2/3}dx

Instead of infinite limits of integration, we have an infinite integrand. evaluating this integral, we have 3.

When we rotate the integral about the x-axis, however, we have pi* ∫ from 0 to 1 1/x^{4/3}dx, which diverges to infinity.

Is this possible? I know that an infinite area can produce a finite volume of revolution, but can the converse of the statement be true? or have I done something wrong?

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# Opposite of Gabriel's Horn Paradox

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