Hi all,

I'm looking at a bonus for an assignment:

Compute the volume of the solid produced when the region between the x-axis and $\displaystyle \[f(x) = \frac{1}{x}\]$, for $\displaystyle \[1 \le x \le \infty \]$, is revolved about the x-axis.

I've never done these types of problems, but I set it up like this:

$\displaystyle \[\begin{array}{l}

\int_{1\,}^{\,\infty } {{x^{ - 1}}} {\rm{d}}x\\

\mathop {\lim }\limits_{t \to \infty } \int_{1\,}^{\,t} {{x^{ - 1}}} {\rm{d}}x\\

\left. {\mathop {\lim }\limits_{t \to \infty } \left[ {\ln x} \right]} \right|_{1\,}^{\,t}\\

\mathop {\lim }\limits_{t \to \infty } \left[ {\ln t - \ln 1} \right]\\

\mathop {\lim }\limits_{t \to \infty } \left[ {\ln t - 0} \right]\\

\ln \infty \\

\infty

\end{array}\]$

Kind of as I expected in my head...the horizontal asymptote on the x-axis would mean that this function is divergent with that infinite limit. Based on that, I wouldn't be able to calculate any volume.

I was wondering if my thinking was right on this or if there is a different procedure I need to take? I simply haven't done any volume problems before. Am I out in left field or is my thinking right?

Thank you in advance!