My professor posed a brain teaser question today, and I cant get it out of my mind. I was hoping the forum can help me make sence of it.(adsbygoogle = window.adsbygoogle || []).push({});

Area under 1/x = infinity:

[tex]A = \int_{1}^{\infty} (1/x)dx[/tex]

[tex]A = \lim_{t\rightarrow \infty} \int_{1}^{t} (1/x)dx[/tex]

[tex]A = \lim_{t\rightarrow \infty} \ln t - \ln 1[/tex]

[tex]A = \infty[/tex]

but the volume of 1/x rotated around the x axis is equal to pi

[tex]V = \pi \int_{1}^{\infty} (1/x)^2dx[/tex]

[tex]V = \pi \lim_{t\rightarrow \infty} \int_{1}^{t} (1/x)^2dx[/tex]

[tex]= \pi \lim_{t\rightarrow \infty} (-1/t + 1/1)[/tex]

[tex]= \pi (1)[/tex]

How can this be true?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Excellent question: A=infinity, V=pi?

**Physics Forums | Science Articles, Homework Help, Discussion**