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$\int_{0}^{π / 2} \sin 2 x \log \tan x dx$ is equal to

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a

π

b

π2

c

0

d

2π

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detailed solution

Correct option is C

Let I=∫0π/2 sin⁡2xlog⁡tan⁡xdx-----i I=∫0π/2 sin⁡2π2−xlog⁡tan⁡π2−xdx ∵∫0a f(x)dx=∫0a f(a−x)dxI=∫0π/2 sin⁡2xlog⁡cot⁡xdx----iiOn adding Eqs. (i) and (ii), we get 2I=∫0π/2 sin⁡2xlog⁡(tan⁡xcot⁡x)dx=∫0π/2 sin⁡2xlog⁡1dx=∫0π/2 0dx⇒ I=0

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