Integral Calculus Question 267
Question: $ \int_{{}}^{{}}{\sqrt{1+\sin \frac{x}{2}}\ dx=} $
[IIT 1980; MP PET 1989; Pb. CET 2003]
Options:
A) $ \frac{1}{4}( \cos \frac{x}{4}-\sin \frac{x}{4} )+c $
B) $ 4( \cos \frac{x}{4}-\sin \frac{x}{4} )+c $
C) $ 4( \sin \frac{x}{4}-\cos \frac{x}{4} )+c $
D) $ 4( \sin \frac{x}{4}+\cos \frac{x}{4} )+c $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_{{}}^{{}}{\sqrt{1+\sin \frac{x}{2},}}dx=\int_{{}}^{{}}{\sqrt{( {{\sin }^{2}}\frac{x}{4}+{{\cos }^{2}}\frac{x}{4}+2\sin \frac{x}{4}\cos \frac{x}{4} )},dx} $ $ =\int_{{}}^{{}}{( \sin \frac{x}{4}+\cos \frac{x}{4} ),dx=4( \sin \frac{x}{4}-\cos \frac{x}{4} )}+c $ .
BETA
