integral from 0 to 9 of (sqrt(x)-1/3 x)

解答

\int_{0}^{9} (x - \frac{1}{3} x) d x

\frac{9}{2}

求解步骤

\int_{0}^{9} x - \frac{1}{3} 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

= \int_{0}^{9} x d x - \int_{0}^{9} \frac{1}{3} x d x

\int_{0}^{9} x d x = 18

\int_{0}^{9} \frac{1}{3} x d x = \frac{27}{2}

= 18 - \frac{27}{2}

化简

18 - \frac{27}{2} : \frac{9}{2}

= \frac{9}{2}

\int e^{2 x} cos (7 x) d x

z \to 1 - i lim (x + i (2 x + y))

\frac{\partial}{\partial x} (sin (π (2 x - y)))

\int x^{7} d x

\frac{d}{d x} (\frac{1 - cos ( x )}{1 + cos ( x )})