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?

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

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