Mathematics - Definite Integration Question with Solution | TestHub

${\int }_{-2}^{2}3\left|x^2-x-2\right|dx$

$=3{\int }_{-2}^2\left|x^2-x-2\right|dx$

$=3\left[{\int }_{-2}^{-1}\left(x^2-x-2\right)dx+{\int }_{-1}^2-\left(x^2-x-2\right)dx\right]$

$=3\left[{\overline{)\left(\frac{x^3}{3}-\frac{x^2}{2}-2x\right)}}_{-2}^{-1}-{\left(\frac{x^3}{3}-\frac{x^2}{2}-2x\right)}_{-1}^2\right]$

$=3\left[7-\frac{2}{3}\right]$

$=19$