A) 0
B) 2
C) 8
D) 4
Correct Answer: C
Solution :
\[\int_{0}^{2\pi }{\sqrt{1+\sin \frac{x}{2}}dx}=\int_{0}^{2\pi }{\left| \sin \frac{x}{4}+\cos \frac{x}{4} \right|dx=4\left[ \sin \frac{x}{4}-\cos \frac{x}{4} \right]}_{0}^{2\pi }\] \[=4[1-0-0+1]=8\].
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