π ∫ 0 1 [ ( 1 ) 2 − ( 1 − y 2 ) 2 ] d y = π [ y − y 5 5 ] | 0 1 = π [ 1 − 1 5 ] = 4 π 5 {\displaystyle \pi \int _{0}^{1}\left[(1)^{2}-(1-y^{2})^{2}\right]dy=\pi \left[y-{\frac {y^{5}}{5}}\right]{\Bigg |}_{0}^{1}=\pi \left[1-{\frac {1}{5}}\right]={\frac {4\pi }{5}}}
![{\displaystyle \pi \int _{0}^{1}\left[(1)^{2}-(1-y^{2})^{2}\right]dy=\pi \left[y-{\frac {y^{5}}{5}}\right]{\Bigg |}_{0}^{1}=\pi \left[1-{\frac {1}{5}}\right]={\frac {4\pi }{5}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/cf94429300c4c7db5c9814f34016d59391102ac8)