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人気のある微分積分 >

integral from 0 to 1/2 of 4e^{2x}

解

\int_{0}^{\frac{1}{2}} 4 e^{2 x} d x

解

2 (e - 1)

+1

十進法表記

3.43656 \dots

解答ステップ

\int_{0}^{\frac{1}{2}} 4 e^{2 x} d x

定数を除く:

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

= 4 \cdot \int_{0}^{\frac{1}{2}} e^{2 x} d x

u置換積分法を適用する

= 4 \cdot \int_{0}^{1} e^{u} \frac{1}{2} d u

定数を除く:

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

= 4 \cdot \frac{1}{2} \cdot \int_{0}^{1} e^{u} d u

共通積分を使用する:

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

= 4 \cdot \frac{1}{2} [e^{u}]_{0}^{1}

簡素化

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

= 2 [e^{u}]_{0}^{1}

限度を計算する:

e - 1

= 2 (e - 1)

グラフ

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