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

解答

\int_{- 1}^{1} x^{2} (1 - ∣ x ∣) d x

\frac{1}{6}

十进制

0.16666 \dots

求解步骤

\int_{- 1}^{1} x^{2} (1 - ∣ x ∣) d x

拿掉绝对值

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

\int_{- 1}^{0} x^{2} (1 - (- x)) d x = \frac{1}{12}

\int_{0}^{1} x^{2} (1 - x) d x = \frac{1}{12}

= \frac{1}{12} + \frac{1}{12}

化简

\frac{1}{12} + \frac{1}{12} : \frac{1}{6}

= \frac{1}{6}

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