integral from-4 to 5 of (|3x^2-12|+x^3)

解答

\int_{- 4}^{5} (3 x^{2} - 12 + x^{3}) d x

\frac{949}{4}

十进制

237.25

求解步骤

\int_{- 4}^{5} 3 x^{2} - 12 + x^{3} d x

拿掉绝对值

= \int_{- 4}^{- 2} 3 x^{2} - 12 + x^{3} d x + \int_{- 2}^{2} - 3 x^{2} + 12 + x^{3} d x + \int_{2}^{5} 3 x^{2} - 12 + x^{3} d x

\int_{- 4}^{- 2} 3 x^{2} - 12 + x^{3} d x = - 28

\int_{- 2}^{2} - 3 x^{2} + 12 + x^{3} d x = 32

\int_{2}^{5} 3 x^{2} - 12 + x^{3} d x = \frac{933}{4}

= - 28 + 32 + \frac{933}{4}

化简

- 28 + 32 + \frac{933}{4} : \frac{949}{4}

= \frac{949}{4}

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