Question

${\int }_0^{2\pi }\sqrt{1+sin\frac{x}{2}}dx=$

• A. 2
• B. 8
• C. 4

Answer 1

Answer: (B)

8

${\int }_0^{2\pi }\sqrt{1+sin\frac{x}{2}}dx={\int }_0^{2\pi }|sin\frac{x}{4}+cos\frac{x}{4}|dx=4{[sin\frac{x}{4}-cos\frac{x}{4}]}_0^{2\pi }$
$=4[1-0-0+1]=8$