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人気のある微分積分 >

integral from 0 to 1 of xf(x^2)

解

\int_{0}^{1} x f (x^{2}) d x

解

\frac{f}{4}

解答ステップ

\int_{0}^{1} x f x^{2} d x

定数を除く:

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

= f \cdot \int_{0}^{1} x x^{2} d x

簡素化

x x^{2} : x^{3}

= f \cdot \int_{0}^{1} x^{3} d x

べき乗則を適用する

= f [\frac{x ^{4}}{4}]_{0}^{1}

限度を計算する:

\frac{1}{4}

= f \frac{1}{4}

簡素化

= \frac{f}{4}

人気の例

integral from x to 2x^2 of ln(t)

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