6.2 Volumes/7: Difference between revisions

Latest revision as of 20:46, 29 November 2022

$y=x^{3}$ , $y=x$ , (x-axis)

$\pi \int _{0}^{1}\left((x)^{2}-(x^{3})^{2})\right)dx$

$=(\pi )\int _{0}^{1}\left((x^{2}-x^{6})\right)dx$

$=\pi ({\frac {x^{3}}{3}}-{\frac {x^{7}}{7}}){\bigg |}_{0}^{1}$

$=\pi ({\frac {1}{3}}-{\frac {1}{7}})$ $={\frac {7\pi }{21}}-{\frac {3\pi }{21}}$ $={\frac {4\pi }{21}}$

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	<math>=\pi(\frac{x^3}{3}-\frac{x^7}{7})\bigg\|_{0}^{1}</math>		<math>=\pi(\frac{x^3}{3}-\frac{x^7}{7})\bigg\|_{0}^{1}</math>

	<math>=\pi(\frac{1}{3}-\frac{1}{7})</math> <math>=\frac{~~7pi~~}{21}-\frac{~~3pi~~}{21}</math> <math>=\frac{~~4pi~~}{21}</math>		<math>=\pi(\frac{1}{3}-\frac{1}{7})</math> <math>=\frac{7\pi}{21}-\frac{3\pi}{21}</math> <math>=\frac{4\pi}{21}</math>