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人気のある微分積分 >

integral from 1 to 2 of 2x(x^2+3)

解

\int_{1}^{2} 2 x (x^{2} + 3) d x

解

\frac{33}{2}

+1

十進法表記

16.5

解答ステップ

\int_{1}^{2} 2 x (x^{2} + 3) d x

定数を除く:

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

= 2 \cdot \int_{1}^{2} x (x^{2} + 3) d x

拡張

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

= 2 \cdot \int_{1}^{2} x^{3} + 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

= 2 (\int_{1}^{2} x^{3} d x + \int_{1}^{2} 3 x d x)

\int_{1}^{2} x^{3} d x = \frac{15}{4}

\int_{1}^{2} 3 x d x = \frac{9}{2}

= 2 (\frac{15}{4} + \frac{9}{2})

簡素化

2 (\frac{15}{4} + \frac{9}{2}) : \frac{33}{2}

= \frac{33}{2}

グラフ

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