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人気のある微分積分 >

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

解

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

解

2 (e^{6} - 1)

+1

十進法表記

804.85758 \dots

解答ステップ

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

定数を除く:

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

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

u置換積分法を適用する

= 6 \cdot \int_{0}^{6} 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

= 6 \cdot \frac{1}{3} \cdot \int_{0}^{6} e^{u} d u

共通積分を使用する:

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

= 6 \cdot \frac{1}{3} [e^{u}]_{0}^{6}

簡素化

6 \cdot \frac{1}{3} [e^{u}]_{0}^{6} : 2 [e^{u}]_{0}^{6}

= 2 [e^{u}]_{0}^{6}

限度を計算する:

e^{6} - 1

= 2 (e^{6} - 1)

グラフ

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