Integral-Calculus Question 517
Question: If $ f(x) $ is an even function, then what is $ \int\limits_0^{\pi }{f(\cos x)dx} $ equal to?
Options:
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
Show Answer
Answer:
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}} $
BETA
