integral from-pi to pi of |x|

解答

\int_{- π}^{π} ∣ x ∣ d x

π^{2}

十进制

9.86960 \dots

求解步骤

\int_{- π}^{π} ∣ x ∣ d x

拿掉绝对值

= \int_{- π}^{0} - x d x + \int_{0}^{π} x d x

\int_{- π}^{0} - x d x = \frac{π ^{2}}{2}

\int_{0}^{π} x d x = \frac{π ^{2}}{2}

= \frac{π ^{2}}{2} + \frac{π ^{2}}{2}

化简

\frac{π ^{2}}{2} + \frac{π ^{2}}{2} : π^{2}

= π^{2}

\frac{\partial}{\partial x} (\frac{1}{( 1 + x ^{2} + y ^{2} )})

d er i v a t i v e f (x) = \frac{2 x}{1 + x ^{2}}

\frac{\partial}{\partial x} (\frac{4 x ^{3}}{x ^{2} + y ^{2}})

\frac{d y}{d x} = 9 y e^{x + 9}

\frac{\partial}{\partial x} (\frac{1}{2 x})