The value of ∫-223x^2-3x-6dx is

Correct answer: 19. ∫-223x^2-x-2dx =3∫-22x^2-x-2dx =3∫-2-1x^2-x-2dx+∫-12-x^2-x-2dx =3x^33-x^22-2x-2-1-x^33-x^22-2x-12 =37-2/3 =19

Q49 / 90 · JEE Main 2021 (25 Feb Shift 2) · Mathematics

The value of $\int_{- 2}^{2} |3 x^{2} - 3 x - 6| d x$ is

Correct answer: 19

$\int_{- 2}^{2} 3 |x^{2} - x - 2| d x$

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

$= 3 [\int_{- 2}^{- 1} (x^{2} - x - 2) d x + \int_{- 1}^{2} - (x^{2} - x - 2) d x]$

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

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

$= 19$

Hence, the correct answer is 19.