$\int_{-2}^{2}\left|3 x^{2}-3 x-6\right| d x$ =

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Professor PC Thomas Classes · Answer

(19) : We have, $\int_{-2}^{2} 3\left|x^{2}-x-2ight| d x$\ $=3\left[\int_{-2}^{-1}\left(x^{2}-x-2ight) d x+\int_{-1}^{2}-\left(x^{2}-x-2ight) d xight]$\ $=3\left[\begin{array}{c}\left(\frac{x^{3}}{3}-\frac{x^{2}}{2}-2 xight)_{-2}^{-1} \ -\left(\frac{x^{3}}{3}-\frac{x^{2}}{2}-2 xight)_{-1}^{2}\end{array}ight]$\ $=3\left[\left(\frac{7}{6}+\frac{4}{6}ight)-\left(\frac{-20}{6}-\frac{7}{6}ight)ight]$\ $=3\left(\frac{11}{6}+\frac{27}{6}ight)=3\left[\frac{38}{6}ight]=19$\