What is the integral from-4 to 8 of |x^2-4x-12| ?

The integral from-4 to 8 of |x^2-4x-12| is 368/3

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integral from-4 to 8 of |x^2-4x-12|

\int_{- 4}^{8} x^{2} - 4 x - 12 d x

\frac{368}{3}

Solution steps

\int_{- 4}^{8} x^{2} - 4 x - 12 d x

Eliminate Absolutes

= \int_{- 4}^{- 2} x^{2} - 4 x - 12 d x + \int_{- 2}^{6} - x^{2} + 4 x + 12 d x + \int_{6}^{8} x^{2} - 4 x - 12 d x

\int_{- 4}^{- 2} x^{2} - 4 x - 12 d x = \frac{56}{3}

\int_{- 2}^{6} - x^{2} + 4 x + 12 d x = \frac{256}{3}

\int_{6}^{8} x^{2} - 4 x - 12 d x = \frac{56}{3}

= \frac{56}{3} + \frac{256}{3} + \frac{56}{3}

Simplify

\frac{56}{3} + \frac{256}{3} + \frac{56}{3} : \frac{368}{3}

= \frac{368}{3}

\int_{6}^{12} \frac{36}{x} d x

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What is the integral from-4 to 8 of |x^2-4x-12| ?
The integral from-4 to 8 of |x^2-4x-12| is 368/3