integral from 0 to 2 of (x-1)^2

解答

\int_{0}^{2} (x - 1)^{2} d x

\frac{2}{3}

十进制

0.66666 \dots

求解步骤

\int_{0}^{2} (x - 1)^{2} d x

乘开

(x - 1)^{2} : x^{2} - 2 x + 1

= \int_{0}^{2} x^{2} - 2 x + 1 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}^{2} x^{2} d x - \int_{0}^{2} 2 x d x + \int_{0}^{2} 1 d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 2 x d x = 4

\int_{0}^{2} 1 d x = 2

= \frac{8}{3} - 4 + 2

化简

\frac{8}{3} - 4 + 2 : \frac{2}{3}

= \frac{2}{3}

d er i v a t i v e 3 5 + 6 x^{6}

\frac{\partial}{\partial x} (5 - x^{2} + x y - 2^{2})

\frac{d}{d x} ((x^{3} + 4)^{- 3})

x \to 0 + lim (6 - \frac{1}{x ^{2}})

d er i v a t i v e y = 4 x^{\frac{2}{3}} + 6 x^{\frac{1}{2}} - 8