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人気のある微分積分 >

integral from 0 to 2 of 2x(x+1)

解

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

解

\frac{28}{3}

+1

十進法表記

9.33333 \dots

解答ステップ

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

定数を除く:

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

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

拡張

x (x + 1) : x^{2} + x

= 2 \cdot \int_{0}^{2} x^{2} + x 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

= 2 (\int_{0}^{2} x^{2} d x + \int_{0}^{2} x d x)

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} x d x = 2

= 2 (\frac{8}{3} + 2)

簡素化

2 (\frac{8}{3} + 2) : \frac{28}{3}

= \frac{28}{3}

グラフ

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