I've encountered a weird problem in my text...somewhat by accident =P(adsbygoogle = window.adsbygoogle || []).push({});

My text only covers volumes of revolution through the disk method, and one of the questions was:

Find the volume of the solid obtained when the given region is rotated about the x-axis.

c) Under y = 1/x from 1 to 4

Using the disk method, I got the answer [tex]\frac{3\pi}{4}[/tex]...

Ok, so I wonder...what happens if I try the shell/rings method?

So this is what I do:

I thought that the radius of such shells would be the height of the function, so it would be "y". And, the length of such shells would be the distance from the function to the line x = 1, ...so (1/y - 1)...

Because of that, I ended up trying this:

[tex]V = \int_{0}^{1} 2\pi \ y\ (\frac{1}{y} - 1) dy [/tex]

This turns out to yield [tex]\pi[/tex]

I'm so confused right now haha...could someone please tell me what I did wrong? Either my shell method was wrong, or the disk method was...or...both =S...

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# Homework Help: Volumes of Revolution

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