Question:
The value of $\int_{2}^{2}\left|3 x^{2}-3 x-6\right| d x$ is
Solution:
$3 \int_{-2}^{2}\left|x^{2}-x-2\right| d x x^{2}-x-2$
$=(x-2)(x+1)$
$=3\left\{\int_{-2}^{-1}\left(x^{2}-x-2\right) d x+\int_{-1}^{2}\left(-x^{2}+x+2\right) d x\right\}$
$=3\left[\left(\frac{x^{3}}{3}-\frac{x^{2}}{2}-2 x\right)_{-2}^{-1}-\left(\frac{x^{3}}{3}-\frac{x^{2}}{2}-2 x\right)_{-1}^{2}\right]$
$=19$
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