A) \[2\sqrt{2}\sin \frac{x}{2}+c\]
B) \[-2\sqrt{2}\sin \frac{x}{2}+c\]
C) \[-2\sqrt{2}\cos \frac{x}{2}+c\]
D) \[2\sqrt{2}\cos \frac{x}{2}+c\]
Correct Answer: A
Solution :
\[I=\int_{{}}^{{}}{\sqrt{1+\cos x}\,dx}=\int_{{}}^{{}}{\sqrt{2{{\cos }^{2}}(x/2)}dx}\] \[I=\sqrt{2}\int_{{}}^{{}}{\cos (x/2\,)dx}=2\sqrt{2}\sin (x/2)+c\].
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