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人気のある微分積分 >

integral from 0 to 8 of 2xe^{-0.2x}

解

\int_{0}^{8} 2 x e^{- 0.2 x} d x

解

23.75345 \dots

解答ステップ

\int_{0}^{8} 2 x e^{- 0.2 x} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{8} x e^{- 0.2 x} d x

u置換積分法を適用する

= 2 \cdot \int_{0}^{- 1.6} \frac{5}{0.2} e^{u} u d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 2 (- \int_{- 1.6}^{0} \frac{5}{0.2} e^{u} u d u)

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 (- \frac{5}{0.2} \cdot \int_{- 1.6}^{0} e^{u} u d u)

簡素化

= 2 (- 25 \cdot \int_{- 1.6}^{0} e^{u} u d u)

部分積分を適用する

= 2 (- 25 [e^{u} u - \int e^{u} d u]_{- 1.6}^{0})

\int e^{u} d u = e^{u}

= 2 (- 25 [e^{u} u - e^{u}]_{- 1.6}^{0})

簡素化

= - 50 [e^{u} u - e^{u}]_{- 1.6}^{0}

限度を計算する:

- 0.47506 \dots

= - 50 (- 0.47506 \dots)

簡素化

= 23.75345 \dots

グラフ

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