QJEEM21Mab0a0: JEE Main 2021 Mathematics - Class 12 JEEM21Mab0a0 Solution

Step-by-Step Verified Solution

x² – x – 2 = (x - 2)(x + 1)



$\int\limits_{ - 2}^2 {3|{x^2} - x - 2|dx}$

$= 3\int\limits_{ - 2}^2 {|{x^2} - x - 2|dx}$

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

$= 3\left[ {\left. {\left( {{{{x^3}} \over 3} - {{{x^2}} \over 2} - 2x} \right)} \right|_{ - 2}^{ - 1} - \left( {{{{x^3}} \over 3} - {{{x^2}} \over 2} - 2x} \right)_{ - 1}^2} \right]$

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

= 19