Mathematics

# The value of$\displaystyle \int_{1}^{2}\frac{\cos \left ( \log x \right )}{x}dx$  is equal to

$\sin \left ( \log 2 \right )$

##### SOLUTION
$\displaystyle \int _{ 1 }^{ 2 } \dfrac { \cos \left( \log x \right) }{ x } dx$

Substitute $\log x=t$
$\displaystyle \frac { 1 }{ x } dx=dt$

$\displaystyle I=\displaystyle \int _{ \log { 1 } }^{ \log { 2 } } \cos { t } dt$

$\displaystyle I={ [\sin { t } ] }_{ \log { 1 } }^{ \log { 2 } }$

$\displaystyle I=\sin { (\log { 2) } }$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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