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人気のある微分積分 >

integral from 0 to 10 of e^{-sqrt(x)}

解

\int_{0}^{10} e^{- x} d x

解

- 2 (- 1 - \frac{- 10 - 1}{e ^{10}})

+1

十進法表記

1.64762 \dots

解答ステップ

\int_{0}^{10} e^{- x} d x

u置換積分法を適用する

= \int_{0}^{- 10} 2 e^{u} u d u

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

= - \int_{- 10}^{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 \cdot \int_{- 10}^{0} e^{u} u d u

部分積分を適用する

= - 2 [e^{u} u - \int e^{u} d u]_{- 10}^{0}

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

= - 2 [e^{u} u - e^{u}]_{- 10}^{0}

限度を計算する:

- 1 - \frac{- 10 - 1}{e ^{10}}

= - 2 (- 1 - \frac{- 10 - 1}{e ^{10}})

グラフ

人気の例

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