Mathematics

Evaluate $\displaystyle\int_{1}^{3}\dfrac{\cos (\log x)}{x}dx$

SOLUTION
Let $t=\log{x}\Rightarrow\,dt=\dfrac{1}{x}dx$

When $x=1\Rightarrow\,t=0$

When $x=3\Rightarrow\,t=\log{3}$

$\displaystyle\int_{1}^{3}{\dfrac{\cos{\left(\log{x}\right)}}{x}dx}$

$=\displaystyle\int_{0}^{\log{3}}{\cos{t}dt}$

$=\left[\sin{t}\right]_{0}^{\log{3}}$

$=\left[\sin{t}\right]_{0}^{\log{3}}$

$=\left[\sin{\log{3}}-\sin{0}\right]$

$=\sin{\log{3}}-0=\sin{\log{3}}$

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

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