integral from-1 to 1 of x^2|x|

解答

\int_{- 1}^{1} x^{2} ∣ x ∣ d x

\frac{1}{2}

十进制

0.5

求解步骤

\int_{- 1}^{1} x^{2} ∣ x ∣ d x

拿掉绝对值

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

\int_{- 1}^{0} x^{2} (- x) d x = \frac{1}{4}

\int_{0}^{1} x^{2} x d x = \frac{1}{4}

= \frac{1}{4} + \frac{1}{4}

化简

\frac{1}{4} + \frac{1}{4} : \frac{1}{2}

= \frac{1}{2}

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