Suppose we want to find the area under f(x) = \frac{1}{x} between x = 1 and \infty:

\int_1^\infty \frac{1}{x} dx = ln(x) |_1^\infty = ln \infty - ln 1 = \infty

(This is technically bad notation, but we’ll correct it later)

Which indicates the area in infinite.

**However**, if we wish to find the volume of the solid created by rotating \frac{1}{x} around the x-axis from x= 1 to \infty, we calculate:

\pi \int_1^\infty (\frac{1}{x})^{2} dx

And what do we get?