Definite Integration Question 10
Question: The value of $ \int_0^{\pi /2}{\log ( \frac{4+3\sin x}{4+3\cos x} )}dx $ is
Options:
A) 2
B) $ \frac{3}{4} $
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ I=\int_0^{\pi /2}{\log ( \frac{4+3\sin x}{4+3\cos x} )}dx. $
Then, $ I=\int_0^{\pi /2}{\log ( \frac{4+3\cos x}{4+3\sin x} )}dx $ , $ [ \because \int_0^{\pi /2}{f(x)dx=\int_0^{\pi /2}{f( \frac{\pi }{2}-x )dx}} ] $
therefore $ I=-\int_0^{\pi /2}{\log ( \frac{4+3\sin x}{4+3\cos x} )dx=-I} $
therefore $ 2I=0\Rightarrow I=0 $ .
BETA
