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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\sqrt {1 + \cos x} \;dx} $ equals
  • ✓
    $2\sqrt 2 \sin \frac{x}{2} + c$
  • B
    $ - 2\sqrt 2 \sin \frac{x}{2} + c$
  • C
    $ - 2\sqrt 2 \cos \frac{x}{2} + c$
  • D
    $2\sqrt 2 \cos \frac{x}{2} + c$
✓

Answer

Correct option: A.
$2\sqrt 2 \sin \frac{x}{2} + c$
a
(a) $I = \int_{}^{} {\sqrt {1 + \cos x} \,dx} = \int_{}^{} {\sqrt {2{{\cos }^2}(x/2)} dx} $
$I = \sqrt 2 \int_{}^{} {\cos (x/2\,)dx} = 2\sqrt 2 \sin (x/2) + c$.

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