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人気のある微分積分 >

integral from 1 to 4 of 6e^{sqrt(x)}

解

\int_{1}^{4} 6 e^{x} d x

解

12 e^{2}

+1

十進法表記

88.66867 \dots

解答ステップ

\int_{1}^{4} 6 e^{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_{1}^{4} e^{x} d x

u置換積分法を適用する

= 6 \cdot \int_{1}^{2} e^{u} \cdot 2 u d u

定数を除く:

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

= 6 \cdot 2 \cdot \int_{1}^{2} e^{u} u d u

部分積分を適用する

= 6 \cdot 2 [e^{u} u - \int e^{u} d u]_{1}^{2}

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

= 6 \cdot 2 [e^{u} u - e^{u}]_{1}^{2}

簡素化

= 12 [e^{u} u - e^{u}]_{1}^{2}

限度を計算する:

e^{2}

= 12 e^{2}

グラフ

人気の例

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