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
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