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STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
MCQ
The value of $\int_{ - 2}^3 {|1 - {x^2}|dx} $ is
  • A
    $\frac{1}{3}$
  • B
    $\frac{{14}}{3}$
  • C
    $\frac{7}{3}$
  • ✓
    $\frac{{28}}{3}$
✓

Answer

Correct option: D.
$\frac{{28}}{3}$
d
(d) $\int_{ - 2}^3 {|1 - {x^2}|dx }$

$={ \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 $

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

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