integral from 0 to 3 of (5-5/3 x)^2

解

\int_{0}^{3} (5 - \frac{5}{3} x)^{2} d x

25

解答ステップ

\int_{0}^{3} (5 - \frac{5}{3} x)^{2} d x

拡張

(5 - \frac{5}{3} x)^{2} : 25 - \frac{50 x}{3} + \frac{25 x ^{2}}{9}

= \int_{0}^{3} 25 - \frac{50 x}{3} + \frac{25 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

= \int_{0}^{3} 25 d x - \int_{0}^{3} \frac{50 x}{3} d x + \int_{0}^{3} \frac{25 x ^{2}}{9} d x

\int_{0}^{3} 25 d x = 75

\int_{0}^{3} \frac{50 x}{3} d x = 75

\int_{0}^{3} \frac{25 x ^{2}}{9} d x = 25

= 75 - 75 + 25

簡素化

= 25