6.2 Volumes/27
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Revision as of 22:20, 25 November 2022 by Kattieh70488@students.laalliance.org (talk | contribs) (Created page with "<math> \begin{align} v=\pi\int_0^1\left[(x^\frac{1}{2})^2-(x^3)^2\right]dx & = \pi\int_0^1\left[(x-x^6)\right]dx \\[2ex] &= \pi\left[\frac{x^2}{2}-\frac{x^7}{7}\right]\Bigg|_0^1 \\[2ex] &= \pi\left[\frac{1}{2}-\frac{1}{7}\right]= \pi\left[\frac{7-2}{14}\right] \\[2ex] &= \frac{5\pi}{14} \end{align} </math>")
![{\displaystyle {\begin{aligned}v=\pi \int _{0}^{1}\left[(x^{\frac {1}{2}})^{2}-(x^{3})^{2}\right]dx&=\pi \int _{0}^{1}\left[(x-x^{6})\right]dx\\[2ex]&=\pi \left[{\frac {x^{2}}{2}}-{\frac {x^{7}}{7}}\right]{\Bigg |}_{0}^{1}\\[2ex]&=\pi \left[{\frac {1}{2}}-{\frac {1}{7}}\right]=\pi \left[{\frac {7-2}{14}}\right]\\[2ex]&={\frac {5\pi }{14}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/b60feb23c871418e2f1f59ecfcd236849c7fdec0)