x = y 2 , x = 1 ; about x=1 {\displaystyle x=y^{2},x=1;{\text{about x=1}}}
π ∫ − 1 1 ( 1 − y 2 ) 2 d y = π ∫ − 1 1 ( 1 − 2 y 2 + y 4 ) d y = π [ y − 2 3 y 3 + y 5 5 ] | − 1 1 = π [ 1 + 2 3 + 1 5 ] − π [ − 1 + 2 5 − 1 5 ] = 16 π 15 {\displaystyle {\begin{aligned}\pi \int _{-1}^{1}\left(1-y^{2}\right)^{2}dy&=\pi \int _{-1}^{1}\left(1-2y^{2}+y^{4}\right)dy\\[2ex]&=\pi \left[y-{\frac {2}{3}}y^{3}+{\frac {y^{5}}{5}}\right]{\Bigg |}_{-1}^{1}\\[2ex]&=\pi \left[1+{\frac {2}{3}}+{\frac {1}{5}}\right]-\pi \left[-1+{\frac {2}{5}}-{\frac {1}{5}}\right]\\[2ex]&={\frac {16\pi }{15}}\end{aligned}}}
![{\displaystyle {\begin{aligned}\pi \int _{-1}^{1}\left(1-y^{2}\right)^{2}dy&=\pi \int _{-1}^{1}\left(1-2y^{2}+y^{4}\right)dy\\[2ex]&=\pi \left[y-{\frac {2}{3}}y^{3}+{\frac {y^{5}}{5}}\right]{\Bigg |}_{-1}^{1}\\[2ex]&=\pi \left[1+{\frac {2}{3}}+{\frac {1}{5}}\right]-\pi \left[-1+{\frac {2}{5}}-{\frac {1}{5}}\right]\\[2ex]&={\frac {16\pi }{15}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/7974c6d7507cf74484b0e00c3a9e2eed715d633e)