integral from 3 to 15 of (5x^2-9)/3

解

\int_{3}^{15} \frac{5 x ^{2} - 9}{3} d x

1824

解答ステップ

\int_{3}^{15} \frac{5 x ^{2} - 9}{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_{3}^{15} 5 x^{2} - 9 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_{3}^{15} 5 x^{2} d x - \int_{3}^{15} 9 d x)

\int_{3}^{15} 5 x^{2} d x = 5580

\int_{3}^{15} 9 d x = 108

= \frac{1}{3} (5580 - 108)

簡素化

\frac{1}{3} (5580 - 108) : 1824

= 1824