Integral-Calculus Question 522
Question: $ \int\limits_0^{2\pi }{\log ( \frac{a+b\sec x}{a-b\sec x} )}dx= $
Options:
A) 0
B) $ \pi /2 $
C) $ \frac{\pi (a+b)}{a-b} $
D) $ \frac{\pi }{2}(a^{2}-b^{2}) $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \int\limits_0^{2\pi }{\log ( \frac{a+b\sec x}{a-b\sec x} )dx} $ $ =2\int\limits_0^{\pi }{\log ( \frac{a+b\sec x}{a-b\sec x} )dx} $ $ =2\int\limits_0^{\pi }{\log (a+b\sec x)dx-2\int\limits_0^{\pi }{\log (a-b\sec (\pi -x))dx}} $ $ =2\int\limits_0^{\pi }{\log (a+b\sec x)dx-2\int\limits_0^{\pi }{\log (a+b\sec ,x)dx=0}} $
BETA
