Hello, Jones!
The area that is limited by the curve $\displaystyle y = \frac{1}{x^2},\;y = 1,\;y = e$ is rotated about the yaxis.
Detirmine the volume of the figure.
The problem: How do i get the integration values?
Since it rotates around the yaxis, i can't use the x values, right?
You can, but it's tricky. Code:

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e + *
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1 +       *
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We can integrate with respect to $\displaystyle y\!:\;\;V \;=\;\pi\int^e_1x^2\,dy$
Since $\displaystyle y = \frac{1}{x^2}$, we have: .$\displaystyle x = \frac{1}{\sqrt{y}}$
Then: .$\displaystyle V \;=\;\pi\int^e_1\left(\frac{1}{\sqrt{y}}\right)^2d y \;=\;\pi\int^e_1\frac{dy}{y} \;= \;\pi\ln(y)\,\bigg]^e_1
$
Therefore: .$\displaystyle V \;=\;\pi\ln(e)  \pi\ln(1)\;=\;\pi(1)  \pi(0) \;= \;\boxed{\pi}$