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人気のある微分積分 >

integral from 1 to 10 of x^2 2/81 (x-1)

解

\int_{1}^{10} x^{2} \frac{2}{81} (x - 1) d x

解

\frac{107}{2}

+1

十進法表記

53.5

解答ステップ

\int_{1}^{10} x^{2} \frac{2}{81} (x - 1) d x

定数を除く:

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

= \frac{2}{81} \cdot \int_{1}^{10} x^{2} (x - 1) d x

拡張

x^{2} (x - 1) : x^{3} - x^{2}

= \frac{2}{81} \cdot \int_{1}^{10} x^{3} - x^{2} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{2}{81} (\int_{1}^{10} x^{3} d x - \int_{1}^{10} x^{2} d x)

\int_{1}^{10} x^{3} d x = \frac{9999}{4}

\int_{1}^{10} x^{2} d x = 333

= \frac{2}{81} (\frac{9999}{4} - 333)

簡素化

\frac{2}{81} (\frac{9999}{4} - 333) : \frac{107}{2}

= \frac{107}{2}

グラフ

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