Mathematics

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


ANSWER

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


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
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