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人気のある微分積分 >

integral from 0 to 2 of 11x(x^2+1)^2

解

\int_{0}^{2} 11 x (x^{2} + 1)^{2} d x

解

\frac{682}{3}

+1

十進法表記

227.33333 \dots

解答ステップ

\int_{0}^{2} 11 x (x^{2} + 1)^{2} d x

定数を除く:

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

= 11 \cdot \int_{0}^{2} x (x^{2} + 1)^{2} d x

拡張

x (x^{2} + 1)^{2} : x^{5} + 2 x^{3} + x

= 11 \cdot \int_{0}^{2} x^{5} + 2 x^{3} + 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

= 11 (\int_{0}^{2} x^{5} d x + \int_{0}^{2} 2 x^{3} d x + \int_{0}^{2} x d x)

\int_{0}^{2} x^{5} d x = \frac{32}{3}

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

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

= 11 (\frac{32}{3} + 8 + 2)

簡素化

11 (\frac{32}{3} + 8 + 2) : \frac{682}{3}

= \frac{682}{3}

グラフ

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