integral from 0 to 2 of (2x-9)(8x^2+2)

解

\int_{0}^{2} (2 x - 9) (8 x^{2} + 2) d x

- 156

解答ステップ

\int_{0}^{2} (2 x - 9) (8 x^{2} + 2) d x

部分積分を適用する

= [(2 x - 9) (\frac{8 x ^{3}}{3} + 2 x) - \int 2 (\frac{8 x ^{3}}{3} + 2 x) d x]_{0}^{2}

\int 2 (\frac{8 x ^{3}}{3} + 2 x) d x = 2 (\frac{2 x ^{4}}{3} + x^{2})

= [(2 x - 9) (\frac{8 x ^{3}}{3} + 2 x) - 2 (\frac{2 x ^{4}}{3} + x^{2})]_{0}^{2}

簡素化

[(2 x - 9) (\frac{8 x ^{3}}{3} + 2 x) - 2 (\frac{2 x ^{4}}{3} + x^{2})]_{0}^{2} : [2 x (2 x^{3} - 12 x^{2} + x - 9)]_{0}^{2}

= [2 x (2 x^{3} - 12 x^{2} + x - 9)]_{0}^{2}

限度を計算する:

- 156

= - 156