integral from 0 to 1 of ((x-sqrt(x))/3)

解答

\int_{0}^{1} (\frac{x - x}{3}) d x

- \frac{1}{18}

十进制

- 0.05555 \dots

求解步骤

\int_{0}^{1} \frac{x - x}{3} d x

提出常数:

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

= \frac{1}{3} \cdot \int_{0}^{1} x - x 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

= \frac{1}{3} (\int_{0}^{1} x d x - \int_{0}^{1} x d x)

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

\int_{0}^{1} x d x = \frac{2}{3}

= \frac{1}{3} (\frac{1}{2} - \frac{2}{3})

化简

\frac{1}{3} (\frac{1}{2} - \frac{2}{3}) : - \frac{1}{18}

= - \frac{1}{18}

d er i v a t i v e cot (x^{6})

\frac{1}{y} \frac{d y}{d x} = e^{x} + lo g_{e} (y)

\int \frac{x}{2 1 + x} d x

a re a x = - y, x = 2 - y^{2}

x \to 6 lim (g (x))