integral from-2 to 2 of (9-|x|^3)

解答

\int_{- 2}^{2} (9 - ∣ x ∣^{3}) d x

28

求解步骤

\int_{- 2}^{2} 9 - ∣ x ∣^{3} d x

拿掉绝对值

= \int_{- 2}^{0} 9 - (- x)^{3} d x + \int_{0}^{2} 9 - x^{3} d x

\int_{- 2}^{0} 9 - (- x)^{3} d x = 14

\int_{0}^{2} 9 - x^{3} d x = 14

= 14 + 14

化简

= 28

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