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

解答

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

25

求解步骤

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

乘开

(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

使用积分加法定则:

\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

化简

= 25

s l o p e (- 10.6) (- 5.8)

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

x \to 3 lim (7)

x \to 1 + lim (\frac{x ^{2} - 1}{x - 1})

y^{^{'}} = \frac{2 - e ^{x}}{3 + 2 y}