A) \[3\]
B) \[2\]
C) \[1\]
D) \[0\]
Correct Answer: D
Solution :
[d] \[f(x)\] is symmetrical about the line \[x=2.\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,f(2-x)=f(2+x)\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,f(x)=f(4-x)\] (Replacing x by \[2-x\]) \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,f'(x)=f'(4-x)\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,I=\int\limits_{0}^{4}{\cos \,(\pi x)f'(x)\,dx}\] \[=\int\limits_{0}^{4}{\cos \,(4\pi -\pi x)\,f'(4-x)\,dx=-I\,\,\,\Rightarrow 2I=0}\]
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