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人気のある微分積分 >

integral from 0 to 1 of 4xe^{-2x^2}

解

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

解

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

+1

十進法表記

0.86466 \dots

解答ステップ

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

u置換積分法を適用する

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

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

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

定数を除く:

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

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

共通積分を使用する:

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

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

簡素化

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

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

限度を計算する:

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

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

グラフ

人気の例

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