Definite Integration Question 351
Question: $ \int_1^{2}{\frac{\cos (\log x)}{x}}dx= $
Options:
A) $ \sin (\log 3) $
B) $ \sin (\log 2) $
C) $ \cos (\log 3) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Put $ t=\log x\Rightarrow dt=\frac{1}{x}dx $ . As $ x=2\Rightarrow t=\log 2 $ and $ x=1\Rightarrow t=0 $ , we have $ \int_1^{2}{\frac{\cos (\log x)}{x}}dx=-\int_0^{\log 2}{\cos tdt}=[\sin t]_0^{\log 2} $
$ =\sin (\log 2) $ .
BETA
