7.2 definite integral — ગણિત ધોરણ 12 સાયન્સ — Question

$={ \int_{ - 2}^{ - 1} {({x^2} - 1)dx + \int_{ - 1}^1 {(1 - {x^2})dx + \int_1^3 {({x^2} - 1)dx} } } } $

$= \left[ {\frac{{{x^2}}}{3} - x} \right]_{ - 2}^{ - 1} + \left[ {x - \frac{{{x^2}}}{3}} \right]_{ - 1}^1 + \left[ {\frac{{{x^2}}}{3} - x} \right]_1^2$

$ = \frac{2}{3} + \frac{2}{3} + 2\left( {\frac{2}{3}} \right) + (9 - 3) - \left( {\frac{1}{3} - 1} \right)$

$ = \frac{{10}}{3} + 6 $

$= \frac{{28}}{3}$.