A) 0
B) \[\int\limits_{0}^{\frac{\pi }{2}}{f(\cos x)dx}\]
C) \[2\int\limits_{0}^{\frac{\pi }{2}}{f(\cos x)dx}\]
D) 1
Correct Answer: C
Solution :
[c] Since \[f(x)\] is an even function therefore \[\int\limits_{0}^{\pi }{f(x)dx=2\int\limits_{0}^{\pi /2}{f(x)dx}}\] Hence, \[\int\limits_{0}^{\pi }{f(\cos x)dx=2\int\limits_{0}^{\pi /2}{f(\cos x)dx}}\]
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