Definite Integration Question 371
Question: $ \int_0^{2\pi }{\sqrt{1+\sin \frac{x}{2}}dx=} $
[MNR 1987; UPSEAT 2000]
Options:
A) 0
B) 2
C) 8
D) 4
Show Answer
Answer:
Correct Answer: C
Solution:
$ \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 $ .
BETA
