∫ 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} = 1 y + 4 y 3 3 + 4 y 2 2 | 1 2 {\displaystyle 1y+{\frac {4y^{3}}{3}}+{\frac {4y^{2}}{2}}{\bigg |}_{1}^{2}} = 2 + 32 3 + 16 2 − ( 1 + 4 3 + 4 2 ) {\displaystyle 2+{\frac {32}{3}}+{\frac {16}{2}}-\left(1+{\frac {4}{3}}+{\frac {4}{2}}\right)} = 49 3 {\displaystyle {\frac {49}{3}}}
