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人気のある微分積分 >

integral from 0 to 2 of 300e^{(3x-4)}

解

\int_{0}^{2} 300 e^{(3 x - 4)} d x

解

100 (e^{2} - \frac{1}{e ^{4}})

+1

十進法表記

737.07404 \dots

解答ステップ

\int_{0}^{2} 300 e^{3 x - 4} d x

定数を除く:

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

= 300 \cdot \int_{0}^{2} e^{3 x - 4} d x

u置換積分法を適用する

= 300 \cdot \int_{- 4}^{2} e^{u} \frac{1}{3} d u

定数を除く:

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

= 300 \cdot \frac{1}{3} \cdot \int_{- 4}^{2} e^{u} d u

共通積分を使用する:

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

= 300 \cdot \frac{1}{3} [e^{u}]_{- 4}^{2}

簡素化

300 \cdot \frac{1}{3} [e^{u}]_{- 4}^{2} : 100 [e^{u}]_{- 4}^{2}

= 100 [e^{u}]_{- 4}^{2}

限度を計算する:

e^{2} - \frac{1}{e ^{4}}

= 100 (e^{2} - \frac{1}{e ^{4}})

グラフ

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