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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_{ - \pi /2}^{\pi /2} {\sqrt {\frac{1}{2}(1 - \cos 2x)} } \,dx = $
  • A
    $0$
  • ✓
    $2$
  • C
    $\frac{1}{2}$
  • D
    None of these
✓

Answer

Correct option: B.
$2$
b
(b) $\int_{ - \pi /2}^{\pi /2} {\sqrt {\frac{1}{2}(1 - \cos 2x)} } \,dx = 2\int_0^{\pi /2} {\,\,\,\,\,|\sin x|dx} $

$= 2[ - \cos x]_0^{\pi /2} = 2\left[ { - \cos \left( {\frac{\pi }{2}} \right) + \cos 0} \right] = 2$.

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