Mathematics

# Find the value of $\int _{ 0 }^{ \pi /2 }{ \sin { 2x } \log { \left( \tan { x } \right) } dx }$

##### SOLUTION
$\displaystyle \int_{a}^{b}f(x)dx=\int_{a}^{b}f(a+b-x)dx$
$\displaystyle I=\int_{0}^{\displaystyle \frac{\pi}{2}}\sin 2x\log(\tan x)dx;I=\int_{0}^{\displaystyle \frac{\pi}{2}}\sin 2(\frac{\pi}{2}-x)\log(\tan (\frac{\pi}{2}-x)dx$
$2I=0\implies I=0$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

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