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人気のある微分積分 >

integral from-2 to 0 of-7e^{-6x-3}

解

\int_{- 2}^{0} - 7 e^{- 6 x - 3} d x

解

- \frac{7 ( e ^{12} - 1 )}{6 e ^{3}}

+1

十進法表記

- 9453.53983 \dots

解答ステップ

\int_{- 2}^{0} - 7 e^{- 6 x - 3} d x

定数を除く:

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

= - 7 \cdot \int_{- 2}^{0} e^{- 6 x - 3} d x

u置換積分法を適用する

= - 7 \cdot \int_{9}^{- 3} - \frac{1}{6} e^{u} d u

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

= - 7 (- \int_{- 3}^{9} - \frac{1}{6} e^{u} d u)

定数を除く:

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

= - 7 (- (- \frac{1}{6} \cdot \int_{- 3}^{9} e^{u} d u))

共通積分を使用する:

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

= - 7 (- (- \frac{1}{6} [e^{u}]_{- 3}^{9}))

簡素化

- 7 (- (- \frac{1}{6} [e^{u}]_{- 3}^{9})) : - \frac{7}{6} [e^{u}]_{- 3}^{9}

= - \frac{7}{6} [e^{u}]_{- 3}^{9}

限度を計算する:

e^{9} - \frac{1}{e ^{3}}

= - \frac{7}{6} (e^{9} - \frac{1}{e ^{3}})

簡素化

= - \frac{7 ( e ^{12} - 1 )}{6 e ^{3}}

グラフ

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