(\integral \_ { 1 } ^ { 2 } \frac { \cos ( \log x ) } { x }... | MATH - FUNDAMENTAL DEFINITE INTEGRATION, DEFINITE INTEGRATION BY SUBSTITUTION | SolveeIt

$\int _ { 1 } ^ { 2 } \frac { \cos ( \log x ) } { x } d x =$

$\sin ( \log 3 )$

$\sin ( \log 2 )$

$\cos ( \log 3 )$

None of these

Answer

$\sin ( \log 2 )$

Explanation

Put $t = \log x \Rightarrow d t = \frac { 1 } { x } d x$ .

As $x = 2 \Rightarrow t = \log 2$ and $x = 1 \Rightarrow t = 0$ , we have

$= \sin ( \log 2 )$ .

Question: \(\int _ { 1 } ^ { 2 } \frac { \cos ( \log x ) } { x } d x =\)...