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人気のある微分積分 >

integral from 3 to 6 of 10000e^{0.02t}

解

\int_{3}^{6} 10000 e^{0.02 t} d t

解

32830.15251 \dots

解答ステップ

\int_{3}^{6} 10000 e^{0.02 t} d t

定数を除く:

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

= 10000 \cdot \int_{3}^{6} e^{0.02 t} d t

u置換積分法を適用する

= 10000 \cdot \int_{0.06}^{0.12} 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

= 10000 \cdot \frac{1}{0.02} \cdot \int_{0.06}^{0.12} e^{u} d u

簡素化

= 10000 \cdot 50 \cdot \int_{0.06}^{0.12} e^{u} d u

共通積分を使用する:

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

= 10000 \cdot 50 [e^{u}]_{0.06}^{0.12}

簡素化

= 500000 [e^{u}]_{0.06}^{0.12}

限度を計算する:

0.06566 \dots

= 500000 \cdot 0.06566 \dots

簡素化

= 32830.15251 \dots

グラフ

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