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人気のある微分積分 >

integral from 2 to 4 of x^2((2x-3))/6

解

\int_{2}^{4} x^{2} \frac{( 2 x - 3 )}{6} d x

解

\frac{32}{3}

+1

十進法表記

10.66666 \dots

解答ステップ

\int_{2}^{4} x^{2} \frac{2 x - 3}{6} d x

定数を除く:

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

= \frac{1}{6} \cdot \int_{2}^{4} x^{2} (2 x - 3) d x

拡張

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

= \frac{1}{6} \cdot \int_{2}^{4} 2 x^{3} - 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{1}{6} (\int_{2}^{4} 2 x^{3} d x - \int_{2}^{4} 3 x^{2} d x)

\int_{2}^{4} 2 x^{3} d x = 120

\int_{2}^{4} 3 x^{2} d x = 56

= \frac{1}{6} (120 - 56)

簡素化

\frac{1}{6} (120 - 56) : \frac{32}{3}

= \frac{32}{3}

グラフ

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