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人気のある微分積分 >

integral from 0 to 0.2 of 25e^{-5y}

解

\int_{0}^{0.2} 25 e^{- 5 y} d y

解

5 (1 - \frac{1}{e})

+1

十進法表記

3.16060 \dots

解答ステップ

\int_{0}^{0.2} 25 e^{- 5 y} d y

定数を除く:

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

= 25 \cdot \int_{0}^{0.2} e^{- 5 y} d y

u置換積分法を適用する

= 25 \cdot \int_{0}^{- 1} - \frac{1}{5} e^{u} d u

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

= 25 (- \int_{- 1}^{0} - \frac{1}{5} e^{u} d u)

定数を除く:

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

= 25 (- (- \frac{1}{5} \cdot \int_{- 1}^{0} e^{u} d u))

共通積分を使用する:

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

= 25 (- (- \frac{1}{5} [e^{u}]_{- 1}^{0}))

簡素化

25 (- (- \frac{1}{5} [e^{u}]_{- 1}^{0})) : 5 [e^{u}]_{- 1}^{0}

= 5 [e^{u}]_{- 1}^{0}

限度を計算する:

1 - \frac{1}{e}

= 5 (1 - \frac{1}{e})

グラフ

人気の例

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