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}{2}\right)-\left(-\frac{1}{1}\right)\right]\Bigg|_1^2\\[2ex] \end{align} }