MCQ
$\int_{-2}^{2}\left|3 x^{2}-3 x-6\right| d x$ નું મૂલ્ય ...... છે.
- ✓$19$
- B$17$
- C$23$
- D$13$
$=3 \int_{-2}^{2}\left|x^{2}-x-2\right| d x$
$=3\left[\int_{-2}^{-1}\left(x^{2}-x-2\right) d x+\int_{-1}^{2}-\left(x^{2}-x-2\right) d x\right]$
$=3\left[\left.\left(\frac{x^{3}}{3}-\frac{x^{2}}{2}-2 x\right)\right|_{-2} ^{-1}-\left(\frac{x^{3}}{3}-\frac{x^{2}}{2}-2 x\right)_{-1}^{2}\right]$
$=3\left[7-\frac{2}{3}\right]$
$=19$
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વિધાન-$2$ : ${\tan ^{ - 1}}\left[ {\frac{{1 + \log {x^2}}}{{1 - \log {x^2}}}} \right]$ = ${\tan ^{ - 1}}\,1 + \,{\tan ^{ - 1}}\left( {\log {x^2}} \right)$