Integral Calculus Question 286
Question: $ \int_{{}}^{{}}{{{( \cos \frac{x}{2}-\sin \frac{x}{2} )}^{2}}dx=} $
Options:
A) $ x+\cos x+c $
B) $ 2{{\cos }^{2}}\frac{x}{2}+c $
C) $ \frac{1}{3}{{( \cos \frac{x}{2}-\frac{x}{2} )}^{3}}+c $
D) $ x-\cos x+c $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int_{{}}^{{}}{{{( \cos \frac{x}{2}-\sin \frac{x}{2} )}^{2}}dx} $ $ =\int_{{}}^{{}}{{ {{\cos }^{2}}\frac{x}{2}+{{\sin }^{2}}\frac{x}{2}-2\sin \frac{x}{2}\cos \frac{x}{2} }}dx $ $ =\int_{{}}^{{}}{(1-\sin x),dx}=x+\cos x+c. $
BETA
