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人気のある微分積分 >

integral from 1 to 2 of-2e^{4t-6}

解

\int_{1}^{2} - 2 e^{4 t - 6} d t

解

- \frac{e ^{4} - 1}{2 e ^{2}}

+1

十進法表記

- 3.62686 \dots

解答ステップ

\int_{1}^{2} - 2 e^{4 t - 6} d t

定数を除く:

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

= - 2 \cdot \int_{1}^{2} e^{4 t - 6} d t

u置換積分法を適用する

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

定数を除く:

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

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

共通積分を使用する:

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

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

簡素化

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

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

限度を計算する:

e^{2} - \frac{1}{e ^{2}}

= - \frac{1}{2} (e^{2} - \frac{1}{e ^{2}})

簡素化

= - \frac{e ^{4} - 1}{2 e ^{2}}

グラフ

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