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人気のある微分積分 >

integral from 0 to 10 of 10e^{0.02x}

解

\int_{0}^{10} 10 e^{0.02 x} d x

解

110.70137 \dots

解答ステップ

\int_{0}^{10} 10 e^{0.02 x} d x

定数を除く:

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

= 10 \cdot \int_{0}^{10} e^{0.02 x} d x

u置換積分法を適用する

= 10 \cdot \int_{0}^{0.2} e^{u} \frac{1}{0.02} d u

定数を除く:

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

= 10 \cdot \frac{1}{0.02} \cdot \int_{0}^{0.2} e^{u} d u

簡素化

= 10 \cdot 50 \cdot \int_{0}^{0.2} e^{u} d u

共通積分を使用する:

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

= 10 \cdot 50 [e^{u}]_{0}^{0.2}

簡素化

= 500 [e^{u}]_{0}^{0.2}

限度を計算する:

0.22140 \dots

= 500 \cdot 0.22140 \dots

簡素化

= 110.70137 \dots

グラフ

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