integral from 2 to 4 of (2(1+x))/(27)

解

\int_{2}^{4} \frac{2 ( 1 + x )}{27} d x

\frac{16}{27}

十進法表記

0.59259 \dots

解答ステップ

\int_{2}^{4} \frac{2 ( 1 + x )}{27} d x

定数を除く:

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

= \frac{2}{27} \cdot \int_{2}^{4} 1 + 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

= \frac{2}{27} (\int_{2}^{4} 1 d x + \int_{2}^{4} x d x)

\int_{2}^{4} 1 d x = 2

\int_{2}^{4} x d x = 6

= \frac{2}{27} (2 + 6)

簡素化

\frac{2}{27} (2 + 6) : \frac{16}{27}

= \frac{16}{27}