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人気のある微分積分 >

integral from 0 to 10 of xe^{(1-x^2)}

解

\int_{0}^{10} x e^{(1 - x^{2})} d x

解

\frac{e ^{100} - 1}{2 e ^{99}}

+1

十進法表記

1.35914 \dots

解答ステップ

\int_{0}^{10} x e^{1 - x^{2}} d x

u置換積分法を適用する

= \int_{1}^{- 99} - \frac{e ^{u}}{2} d u

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

= - \int_{- 99}^{1} - \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_{- 99}^{1} 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}]_{- 99}^{1})

簡素化

= \frac{1}{2} [e^{u}]_{- 99}^{1}

限度を計算する:

e - \frac{1}{e ^{99}}

= \frac{1}{2} (e - \frac{1}{e ^{99}})

簡素化

= \frac{e ^{100} - 1}{2 e ^{99}}

グラフ

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