A) \[\frac{g(x)}{g(\pi )}\]
B) \[g(x)+g(\pi )\]
C) \[g(x)-g(\pi )\]
D) \[g(x).\,g(\pi )\]
Correct Answer: B
Solution :
\[g(x+\pi )=\int\limits_{0}^{x+\pi }{\cos 4\,dt=g(x)+\int\limits_{0}^{\pi }{\cos 4t\,dt}}\] \[=g(x)+g(\pi )\] Here \[g(\pi )=\int\limits_{0}^{\pi }{\cos 4t\,dt=0}\] so answers are (b) or (c)
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