∫ 1 2 ( 1 + 2 y 2 ) d y {\displaystyle \int _{1}^{2}\left(1+2y^{2}\right)dy} = ∫ 1 2 ( 4 y 2 + 4 y + 1 ) d y {\displaystyle \int _{1}^{2}\left(4y^{2}+4y+1\right)dy} = 4 y 3 3 + 4 y 2 2 | 1 2 {\displaystyle {\frac {4y^{3}}{3}}+{\frac {4y^{2}}{2}}{\bigg |}_{1}^{2}} = 32 3 {\displaystyle {\frac {32}{3}}}
