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人気のある微分積分 >

integral from 0 to 1 of 2/5 x^2(x+2)

解

\int_{0}^{1} \frac{2}{5} x^{2} (x + 2) d x

解

\frac{11}{30}

+1

十進法表記

0.36666 \dots

解答ステップ

\int_{0}^{1} \frac{2}{5} x^{2} (x + 2) d x

定数を除く:

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

= \frac{2}{5} \cdot \int_{0}^{1} x^{2} (x + 2) d x

部分積分を適用する

= \frac{2}{5} [\frac{1}{3} x^{3} (x + 2) - \int \frac{x ^{3}}{3} d x]_{0}^{1}

\int \frac{x ^{3}}{3} d x = \frac{x ^{4}}{12}

= \frac{2}{5} [\frac{1}{3} x^{3} (x + 2) - \frac{x ^{4}}{12}]_{0}^{1}

簡素化

\frac{2}{5} [\frac{1}{3} x^{3} (x + 2) - \frac{x ^{4}}{12}]_{0}^{1} : \frac{2}{5} [\frac{3 x ^{4} + 8 x ^{3}}{12}]_{0}^{1}

= \frac{2}{5} [\frac{3 x ^{4} + 8 x ^{3}}{12}]_{0}^{1}

限度を計算する:

\frac{11}{12}

= \frac{2}{5} \cdot \frac{11}{12}

簡素化

= \frac{11}{30}

グラフ

人気の例

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\int \frac{1}{e ^{- 4 x}} d x

limit as x approaches 2 of (x-5)/(x-2)

x \to 2 lim (\frac{x - 5}{x - 2})

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x \to 0 lim (\frac{z ^{x} - 1}{x})

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derivative of (x^{-2}+x^{-3}(x^5-9x^2))

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