integral from 2 to 5 of ((5x+2))/3

解

\int_{2}^{5} \frac{( 5 x + 2 )}{3} d x

\frac{39}{2}

十進法表記

19.5

解答ステップ

\int_{2}^{5} \frac{5 x + 2}{3} d x

定数を除く:

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

= \frac{1}{3} \cdot \int_{2}^{5} 5 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}{3} (\int_{2}^{5} 5 x d x + \int_{2}^{5} 2 d x)

\int_{2}^{5} 5 x d x = \frac{105}{2}

\int_{2}^{5} 2 d x = 6

= \frac{1}{3} (\frac{105}{2} + 6)

簡素化

\frac{1}{3} (\frac{105}{2} + 6) : \frac{39}{2}

= \frac{39}{2}