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人気のある微分積分 >

integral from 0 to a of xe^{x/a}

解

\int_{0}^{a} x e^{\frac{x}{a}} d x

解

a^{2}

解答ステップ

\int_{0}^{a} x e^{\frac{x}{a}} d x

部分積分を適用する

= [a e^{\frac{x}{a}} x - \int a e^{\frac{x}{a}} d x]_{0}^{a}

\int a e^{\frac{x}{a}} d x = a^{2} e^{\frac{x}{a}}

= [a e^{\frac{x}{a}} x - a^{2} e^{\frac{x}{a}}]_{0}^{a}

限度を計算する:

a^{2}

= a^{2}

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