y = x 3 {\displaystyle y=x^{3}} , y = x {\displaystyle y=x} , (x-axis)
π ∫ 0 1 ( ( x ) 2 − ( x 3 ) 2 ) ) d x {\displaystyle \pi \int _{0}^{1}\left((x)^{2}-(x^{3})^{2})\right)dx}
= ( π ) ∫ 0 1 ( ( x 2 − x 6 ) ) d x {\displaystyle =(\pi )\int _{0}^{1}\left((x^{2}-x^{6})\right)dx}
= π ( x 3 3 − x 7 7 ) | 0 1 {\displaystyle =\pi ({\frac {x^{3}}{3}}-{\frac {x^{7}}{7}}){\bigg |}_{0}^{1}}
= π ( 1 3 − 1 7 ) {\displaystyle =\pi ({\frac {1}{3}}-{\frac {1}{7}})} = 7 π 21 − 3 π 21 {\displaystyle ={\frac {7\pi }{21}}-{\frac {3\pi }{21}}} = 4 π 21 {\displaystyle ={\frac {4\pi }{21}}}
