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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_{ - 2}^2 {|1 - {x^2}|\,dx = } $
 
  • A
    $2$
  • ✓
    $4$
  • C
    $6$
  • D
    $8$
✓

Answer

Correct option: B.
$4$
b
(b) $\int_{-2}^{-1}{|1-{{x}^{2}}|\,dx+\int_{-1}^{1}{|1-{{x}^{2}}|\,dx-\int_{1}^{2}{|1-{{x}^{2}}|\,dx}}}$

$ + \int_1^2 {|1 - {x^2}|dx} $

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

$= \frac{4}{3} + \frac{4}{3} + \frac{4}{3} = 4.$

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