6.2 Volumes/7

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

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

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

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

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