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. So the other day I stumbled upon a particular interesting integral: ∫ from 0 to 1 1/x2/3 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/x4/3 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?