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人気のある微分積分 >

integral from 0 to 2 of xe^{4-x^2}

解

\int_{0}^{2} x e^{4 - x^{2}} d x

解

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

+1

十進法表記

26.79907 \dots

解答ステップ

\int_{0}^{2} x e^{4 - x^{2}} d x

u置換積分法を適用する

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

定数を除く:

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

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

共通積分を使用する:

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

= - (- \frac{1}{2} [e^{u}]_{0}^{4})

簡素化

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

限度を計算する:

e^{4} - 1

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

簡素化

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

グラフ

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