6.2 Volumes/3

$y={\frac {1}{x}},x=1,x=2,y=0;{\text{about the x-axis}}$

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \pi\int_1^2\left[\left(\frac{1}{x}\right)^2\right]dx & = \pi\int_1^2\left[\left(\frac{1}{x^2}\right)\right]dx \\[2ex] &= \pi\left[-\frac{1}{x}\right]\Bigg|_1^2\\[2ex] &= \pi\left[\left(-\frac{1}{\left(2\right)}\right)-\left(-\frac{1}{\left(1\right)}\right)\right] \\[2ex] &= \pi\left[-\frac{1}{2}+1\right= \pi\left[\frac{1}{2}\right] \\[2ex] &= \frac{\pi}{2} \\[2ex] \end{align} }