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人気のある微分積分 >

integral from 2 to 4 of 4e^{5x-8}

解

\int_{2}^{4} 4 e^{5 x - 8} d x

解

\frac{4 ( e ^{12} - e ^{2} )}{5}

+1

十進法表記

130197.92189 \dots

解答ステップ

\int_{2}^{4} 4 e^{5 x - 8} d x

定数を除く:

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

= 4 \cdot \int_{2}^{4} e^{5 x - 8} d x

u置換積分法を適用する

= 4 \cdot \int_{2}^{12} e^{u} \frac{1}{5} d u

定数を除く:

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

= 4 \cdot \frac{1}{5} \cdot \int_{2}^{12} e^{u} d u

共通積分を使用する:

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

= 4 \cdot \frac{1}{5} [e^{u}]_{2}^{12}

簡素化

4 \cdot \frac{1}{5} [e^{u}]_{2}^{12} : \frac{4}{5} [e^{u}]_{2}^{12}

= \frac{4}{5} [e^{u}]_{2}^{12}

限度を計算する:

e^{12} - e^{2}

= \frac{4}{5} (e^{12} - e^{2})

簡素化

= \frac{4 ( e ^{12} - e ^{2} )}{5}

グラフ

人気の例

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\int_{5}^{6} \frac{1}{( x - 5 ) ^{\frac{4}{3}}} d x

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\int_{0}^{1} e^{x y} d y

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integral from 0 to 3 of 6-3y^2

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