MCQ
$\int_{\,0}^{\,\pi } {\sqrt {\frac{{1 + \cos 2x}}{2}} \,dx} $ is equal to
- A$0$
- ✓$2$
- C$1$
- D$ - 1$
$I = \int_{\,0}^{\,\pi /2} {\cos x\,dx} - \int_{\,\pi /2}^{\,\pi } {\cos x\,dx} $
$= [\sin x]_0^{\pi /2} - [\sin x]_{\pi /2}^\pi $
$I = \left[ {\sin \frac{\pi }{2} - \sin 0} \right] - \left[ {\sin \pi - \sin \frac{\pi }{2}} \right] $
$=1+ 1 = 2.$
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