6.2 Volumes/3

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle y=\frac{1}{x}, x = 1, x = 2, y = 0; \text{about the x-axis} }

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\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]{\Bigg |}_{1}^{2}\\[2ex]&=\pi \left[-{\frac {1}{2}}+1\right]{\Bigg |}_{1}^{2}\\[2ex]=\pi \left[{\frac {1}{2}}\right]&={\frac {\pi }{2}}\end{aligned}}}