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人気のある微分積分 >

integral from 0 to 3 of (xe^{x^2})/3

解

\int_{0}^{3} \frac{x e ^{x^{2}}}{3} d x

解

\frac{e ^{9} - 1}{6}

+1

十進法表記

1350.34732 \dots

解答ステップ

\int_{0}^{3} \frac{x e ^{x^{2}}}{3} d x

定数を除く:

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

= \frac{1}{3} \cdot \int_{0}^{3} x e^{x^{2}} d x

u置換積分法を適用する

= \frac{1}{3} \cdot \int_{0}^{9} \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}{3} \cdot \frac{1}{2} \cdot \int_{0}^{9} e^{u} d u

共通積分を使用する:

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

= \frac{1}{3} \cdot \frac{1}{2} [e^{u}]_{0}^{9}

簡素化

\frac{1}{3} \cdot \frac{1}{2} [e^{u}]_{0}^{9} : \frac{1}{6} [e^{u}]_{0}^{9}

= \frac{1}{6} [e^{u}]_{0}^{9}

限度を計算する:

e^{9} - 1

= \frac{1}{6} (e^{9} - 1)

簡素化

= \frac{e ^{9} - 1}{6}

グラフ

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