integral from 0 to 3 of c*(3-x)

解

\int_{0}^{3} c \cdot (3 - x) d x

\frac{9}{2} c

解答ステップ

\int_{0}^{3} c (3 - x) d x

定数を除く:

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

= c \cdot \int_{0}^{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

= c (\int_{0}^{3} 3 d x - \int_{0}^{3} x d x)

\int_{0}^{3} 3 d x = 9

\int_{0}^{3} x d x = \frac{9}{2}

= c (9 - \frac{9}{2})

結合

9 - \frac{9}{2} : \frac{9}{2}

= \frac{9}{2} c